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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
<｜begin▁of▁sentence｜><｜User｜>If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this equation: x times (x plus y) equals x squared plus 8. I need to find the value of xy. Hmm, let's write that down ste... | deepscaler_teacher_vllm_clean_v4_conceptual | math | If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? | 8 | <｜begin▁of▁sentence｜><｜User｜>If $x \cdot (x+y) = x^2 + 8$, what is the value of $xy$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this equation: x times (x plus y) equals x squared plus 8. I need to find the value of xy. Hmm, let's write that down step by step.
First, let's parse the equation: x*(x + y) = x² + 8.
I think I should start by expanding the left side. So, x*(x + y) is equal to x² + xy. That makes sense becaus... | official | v4_conceptual | 17,168 | 914 | 1f89263f69f12d84 | 8 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x \\cdot (x+y) = x^2 + 8$, what is the value of $xy$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this equation: x times (x plus y) equals x square... | 927 |
<｜begin▁of▁sentence｜><｜User｜>A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out how many diagonals a convex decagon has. Hmm, ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? | 35 | <｜begin▁of▁sentence｜><｜User｜>A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out how many diagonals a convex decagon has. Hmm, I remember that the number of diagonals in a polygon can be found using a formula. Wait, let me recall... I think it's something like n(n-3)/2, where n is the number of sides. Let me verify that because I might be mixing it up with some... | official | v4_conceptual | 39,721 | 1,018 | 42cb164c3db33c88 | 35 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square has two diagonals, and a convex pentagon has five diagonals. How many diagonals does a convex decagon have?",
"role": "user"
},
{
"content": "<think>\nOkay,... | 1,031 |
<｜begin▁of▁sentence｜><｜User｜>Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? | m = 1 | <｜begin▁of▁sentence｜><｜User｜>Given the function $f(x) = \frac{m}{x} - m + \ln x$ (where $m$ is a constant).
1. Find the monotonic intervals of $f(x)$.
2. For what values of $m$ does $f(x) \geq 0$ hold true? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this function f(x) = m/x - m + ln x, and I need to do two things: first, find its monotonic intervals, and second, determine for which values of m the inequality f(x) ≥ 0 holds. Hmm, let's start with the first part.
1. **Finding Monotonic Intervals:**
To find the monotonic intervals of f(x), I... | official | v4_conceptual | 14,716 | 3,028 | 5b56eb4dac6e25a5 | 1 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = \\frac{m}{x} - m + \\ln x$ (where $m$ is a constant).\n1. Find the monotonic intervals of $f(x)$.\n2. For what values of $m$ does $f(x) \\geq 0$ hold t... | 3,041 |
<｜begin▁of▁sentence｜><｜User｜>What is the value of the expression $x^2+ 5x-6$, when $x =-1$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this math problem here: I need to find the value of the expression \(x^2 + 5x - 6\) when \(x = -1\). Hmm, let me th... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the value of the expression $x^2+ 5x-6$, when $x =-1$? | -10 | <｜begin▁of▁sentence｜><｜User｜>What is the value of the expression $x^2+ 5x-6$, when $x =-1$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this math problem here: I need to find the value of the expression \(x^2 + 5x - 6\) when \(x = -1\). Hmm, let me think about how to approach this step by step.
First, I remember that when you have an expression like this, you substitute the given value of \(x\) into the expression and then perf... | official | v4_conceptual | 17,054 | 1,501 | b9f61f50c5f07716 | -10 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of the expression $x^2+ 5x-6$, when $x =-1$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this math problem here: I need to find the v... | 1,514 |
<｜begin▁of▁sentence｜><｜User｜>Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the distance between the vertices of the hyperbola given by the equation \(9x^2... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the distance between the vertices of the hyperbola given by the equation \(9x^2 + 54x - y^2 + 10y + 55 = 0\). Hmm, hyperbolas can be a bit tricky, but I remember that the standard form of a hyperbola is either \(\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\) or \(\frac{(y-k)^2}{b^2} - \... | official | v4_conceptual | 18,183 | 3,050 | 5106d0236a805b5b | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the distance between the vertices of the hyperbola $9x^2 + 54x - y^2 + 10y + 55 = 0.$",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the dist... | 3,063 |
<｜begin▁of▁sentence｜><｜User｜>Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. Let's think step by step a... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction. Let's think step by step a... | <think>
Okay, so I need to find the probability that the sum of two numbers is less than their product, given that exactly one of the numbers must be even when selecting two numbers from the set of positive integers less than or equal to 6. Let me break this down step by step.
First, let's understand the setup. The se... | official | v4_conceptual | 8,811 | 3,526 | 5ddf6f5b5588edbb | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two numbers are independently selected from the set of positive integers less than or equal to 6. Exactly one of the numbers must be even. What is the probability that the sum of... | 3,539 |
<｜begin▁of▁sentence｜><｜User｜>A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. Let's think step b... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. | 927 | <｜begin▁of▁sentence｜><｜User｜>A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determine the number of possible delivery sequences available to the paperboy under these conditions. Let's think step b... | <think>
Okay, so I have this problem about a paperboy delivering newspapers to 11 houses on Main Street. He can choose to skip delivering to any house, but he must not skip three consecutive houses. I need to figure out how many possible delivery sequences he can have under these conditions.
Hmm, let me try to underst... | official | v4_conceptual | 3,927 | 2,527 | 00fa760bcebe13d2 | 927 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determi... | 2,540 |
<｜begin▁of▁sentence｜><｜User｜>In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the maximum value of $k$ . | 2012 | <｜begin▁of▁sentence｜><｜User｜>In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatever the arrangement of the edges, from every vertex we can reach $k$ vertices using at most two edges. Find the ... | <think>
Okay, so I have this problem about a directed graph with 2013 vertices. The problem states that there's exactly one edge between any two vertices, which means it's a complete directed graph, right? Because in a complete graph, every pair of vertices is connected by a single edge. Now, it also says that for ever... | official | v4_conceptual | 30,823 | 2,187 | 1d0219bff9e081c0 | 2012 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatev... | 2,200 |
<｜begin▁of▁sentence｜><｜User｜>Simplify $\sqrt{28x} \cdot \sqrt{15x} \cdot \sqrt{21x}$. Express your answer in simplest radical form in terms of $x$.
Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter $\sqrt{14}$ as "sqrt(14)" or "sqrt{14}... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Simplify $\sqrt{28x} \cdot \sqrt{15x} \cdot \sqrt{21x}$. Express your answer in simplest radical form in terms of $x$.
Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter $\sqrt{14}$ as "sqrt(14)" or "sqrt{14}". | 42x\sqrt{5x} | <｜begin▁of▁sentence｜><｜User｜>Simplify $\sqrt{28x} \cdot \sqrt{15x} \cdot \sqrt{21x}$. Express your answer in simplest radical form in terms of $x$.
Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter $\sqrt{14}$ as "sqrt(14)" or "sqrt{14}... | <think>
Okay, so I need to simplify the expression √(28x) · √(15x) · √(21x). Hmm, let me think about how to approach this. I remember that when you multiply square roots together, you can combine them under a single square root by multiplying the expressions inside. So, that would mean √(28x) * √(15x) * √(21x) is equal... | official | v4_conceptual | 37,078 | 2,802 | 5e0383c43c78b5aa | 42x\sqrt{5x} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\sqrt{28x} \\cdot \\sqrt{15x} \\cdot \\sqrt{21x}$. Express your answer in simplest radical form in terms of $x$.\n\nNote: When entering a square root with more than on... | 2,815 |
<｜begin▁of▁sentence｜><｜User｜>Find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} + 1\frac{2}{3} \right)$. Express your answer as a mixed number. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this math problem here: 53 multiplie... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} + 1\frac{2}{3} \right)$. Express your answer as a mixed number. | -15\frac{3}{5} | <｜begin▁of▁sentence｜><｜User｜>Find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} + 1\frac{2}{3} \right)$. Express your answer as a mixed number. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this math problem here: 53 multiplied by (3 and 1/5 minus 4 and 1/2), then divided by (2 and 3/4 plus 1 and 2/3). Hmm, that looks a bit complicated, but I think I can break it down step by step.
First, let me write down the problem again to make sure I have it right:
53 · (3 1/5 - 4 1/2) ÷ (2 ... | official | v4_conceptual | 19,301 | 2,754 | 8027e69ef8ec6f0b | -15 \dfrac{3}{5} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find $53\\cdot\\left(3\\frac{1}{5} - 4\\frac{1}{2}\\right) \\div \\left(2\\frac{3}{4} + 1\\frac{2}{3} \\right)$. Express your answer as a mixed number.",
"role": "user"
},
... | 2,767 |
<｜begin▁of▁sentence｜><｜User｜>Let $a, b \in \mathbb{R}$. If the line $l: ax+y-7=0$ is transformed by the matrix $A= \begin{bmatrix} 3 & 0 \\ -1 & b\end{bmatrix}$, and the resulting line is $l′: 9x+y-91=0$. Find the values of the real numbers $a$ and $b$. Let's think step by step and output the final answer within \boxed... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let $a, b \in \mathbb{R}$. If the line $l: ax+y-7=0$ is transformed by the matrix $A= \begin{bmatrix} 3 & 0 \\ -1 & b\end{bmatrix}$, and the resulting line is $l′: 9x+y-91=0$. Find the values of the real numbers $a$ and $b$. | 13 | <｜begin▁of▁sentence｜><｜User｜>Let $a, b \in \mathbb{R}$. If the line $l: ax+y-7=0$ is transformed by the matrix $A= \begin{bmatrix} 3 & 0 \\ -1 & b\end{bmatrix}$, and the resulting line is $l′: 9x+y-91=0$. Find the values of the real numbers $a$ and $b$. Let's think step by step and output the final answer within \boxed... | <think>
Okay, so I have this problem where I need to find the values of real numbers a and b. The problem says that the line l: ax + y - 7 = 0 is transformed by the matrix A = [[3, 0], [-1, b]], and the resulting line is l': 9x + y - 91 = 0. I need to find a and b.
Hmm, let me start by understanding what's being asked... | official | v4_conceptual | 9,707 | 1,546 | abc5d68522bf58f1 | 13 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a, b \\in \\mathbb{R}$. If the line $l: ax+y-7=0$ is transformed by the matrix $A= \\begin{bmatrix} 3 & 0 \\\\ -1 & b\\end{bmatrix}$, and the resulting line is $l′: 9x+y-91=... | 1,559 |
<｜begin▁of▁sentence｜><｜User｜>If six geometric means are inserted between $16$ and $11664$, calculate the sixth term in the geometric series. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: If six geometric means are inserted between 16 ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | If six geometric means are inserted between $16$ and $11664$, calculate the sixth term in the geometric series. | 3888 | <｜begin▁of▁sentence｜><｜User｜>If six geometric means are inserted between $16$ and $11664$, calculate the sixth term in the geometric series. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: If six geometric means are inserted between 16 and 11664, calculate the sixth term in the geometric series. Hmm, let me try to understand what this means.
First, when they say "six geometric means are inserted between 16 and 11664," I think that means we're creating a geometr... | official | v4_conceptual | 31,764 | 3,991 | 5ee7467cabc61874 | 3888 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If six geometric means are inserted between $16$ and $11664$, calculate the sixth term in the geometric series.",
"role": "user"
},
{
"content": "<think>\nOkay, so I ... | 4,004 |
<｜begin▁of▁sentence｜><｜User｜>Let $S = \{1, 2,..., 8\}$ . How many ways are there to select two disjoint subsets of $S$ ? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: Given the set S = {1, 2, ..., 8}, how many ways are there to select tw... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let $S = \{1, 2,..., 8\}$ . How many ways are there to select two disjoint subsets of $S$ ? | 6561 | <｜begin▁of▁sentence｜><｜User｜>Let $S = \{1, 2,..., 8\}$ . How many ways are there to select two disjoint subsets of $S$ ? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: Given the set S = {1, 2, ..., 8}, how many ways are there to select two disjoint subsets of S? Hmm, let me try to figure this out step by step.
First, I need to understand what the question is asking. It says "select two disjoint subsets of S". So, we have the set S with elements ... | official | v4_conceptual | 10,268 | 3,030 | acb62f9c9b6041ed | 6561 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S = \\{1, 2,..., 8\\}$ . How many ways are there to select two disjoint subsets of $S$ ?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this proble... | 3,043 |
<｜begin▁of▁sentence｜><｜User｜>In a large library storage room, there are $1584$ boxes, each containing $45$ books. The library dean asks for these books to be repacked so that each new box contains $47$ books. How many books will be left over after repacking the books into as many full boxes of $47$ books each as possib... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In a large library storage room, there are $1584$ boxes, each containing $45$ books. The library dean asks for these books to be repacked so that each new box contains $47$ books. How many books will be left over after repacking the books into as many full boxes of $47$ books each as possible? | 28 | <｜begin▁of▁sentence｜><｜User｜>In a large library storage room, there are $1584$ boxes, each containing $45$ books. The library dean asks for these books to be repacked so that each new box contains $47$ books. How many books will be left over after repacking the books into as many full boxes of $47$ books each as possib... | <think>
Okay, so I have this problem here about repacking books from boxes in a library storage room. Let me try to understand it step by step.
First, there are 1584 boxes, each containing 45 books. The library dean wants to repack these books so that each new box contains 47 books. The question is asking how many boo... | official | v4_conceptual | 28,428 | 2,606 | 2ff775c692452cca | 28 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a large library storage room, there are $1584$ boxes, each containing $45$ books. The library dean asks for these books to be repacked so that each new box contains $47$ books... | 2,619 |
<｜begin▁of▁sentence｜><｜User｜>Assuming $a \neq 3$, $b \neq 4$, and $c \neq 5$, what is the value in simplest form of the following expression?
\[\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}\] Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Assuming $a \neq 3$, $b \neq 4$, and $c \neq 5$, what is the value in simplest form of the following expression?
\[\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}\] | -1 | <｜begin▁of▁sentence｜><｜User｜>Assuming $a \neq 3$, $b \neq 4$, and $c \neq 5$, what is the value in simplest form of the following expression?
\[\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}\] Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out the value of this expression:
\[
\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}
\]
Given that \( a \neq 3 \), \( b \neq 4 \), and \( c \neq 5 \). Hmm, the problem is asking for the value in its simplest form. Since there are variables in the numerator and denominator... | official | v4_conceptual | 337 | 2,390 | 86d92ff7a731dfc9 | -1 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assuming $a \\neq 3$, $b \\neq 4$, and $c \\neq 5$, what is the value in simplest form of the following expression?\n\\[\\frac{a-3}{5-c} \\cdot \\frac{b-4}{3-a} \\cdot \\frac{c-5... | 2,403 |
<｜begin▁of▁sentence｜><｜User｜>The value of \(987 + 113 - 1000\) is Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, let me try to solve this problem: \(987 + 113 - 1000\). Hmm, so I need to calculate the sum of 987 and 113 first, and then subtract 1000 from the resul... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The value of \(987 + 113 - 1000\) is | 100 | <｜begin▁of▁sentence｜><｜User｜>The value of \(987 + 113 - 1000\) is Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, let me try to solve this problem: \(987 + 113 - 1000\). Hmm, so I need to calculate the sum of 987 and 113 first, and then subtract 1000 from the result. Let me take it step by step.
First, let me add 987 and 113. Hmm, adding these two numbers together. Maybe I can break it down to make it easier. Let's ... | official | v4_conceptual | 4,310 | 2,129 | aa92f07ad129d650 | 100 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The value of \\(987 + 113 - 1000\\) is",
"role": "user"
},
{
"content": "<think>\nOkay, let me try to solve this problem: \\(987 + 113 - 1000\\). Hmm, so I need to ca... | 2,142 |
<｜begin▁of▁sentence｜><｜User｜>Lily pads $1,2,3,\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Lily pads $1,2,3,\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\tfrac{p}{q}$, where ... | 107 | <｜begin▁of▁sentence｜><｜User｜>Lily pads $1,2,3,\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad ... | <think>
Okay, so I have this problem where a frog starts on pad 1 and jumps either to pad k+1 or k+2 each time, each with probability 1/2. I need to find the probability that the frog will eventually visit pad 7. The answer should be in the form p/q where p and q are coprime, and then find p+q.
First, let me try to un... | official | v4_conceptual | 23,778 | 3,308 | cca7876d98e1b507 | 107 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lily pads $1,2,3,\\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen ra... | 3,321 |
<｜begin▁of▁sentence｜><｜User｜>Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \frac {1}{z} = 5,$ and $y + \frac {1}{x} = 29.$ Then $z + \frac {1}{y} = \frac {m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
note: this is the type of pro... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \frac {1}{z} = 5,$ and $y + \frac {1}{x} = 29.$ Then $z + \frac {1}{y} = \frac {m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
note: this is the type of problem that makes you think sym... | 5 | <｜begin▁of▁sentence｜><｜User｜>Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \frac {1}{z} = 5,$ and $y + \frac {1}{x} = 29.$ Then $z + \frac {1}{y} = \frac {m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
note: this is the type of pro... | <think>
Okay, so I have this problem where I need to find the value of \( z + \frac{1}{y} \) given three equations: \( xyz = 1 \), \( x + \frac{1}{z} = 5 \), and \( y + \frac{1}{x} = 29 \). The answer should be in the form \( \frac{m}{n} \) where m and n are coprime, and then find \( m + n \).
First, let's write down ... | official | v4_conceptual | 23,488 | 2,907 | 8f5e5ba230276e34 | 5 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \\frac {1}{z} = 5,$ and $y + \\frac {1}{x} = 29.$ Then $z + \\frac {1}{y} = \... | 2,920 |
<｜begin▁of▁sentence｜><｜User｜>Bill can buy mags, migs, and mogs for $\$3$, $\$4$, and $\$8$ each, respectively. What is the largest number of mogs he can purchase if he must buy at least one of each item and will spend exactly $\$100$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><th... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Bill can buy mags, migs, and mogs for $\$3$, $\$4$, and $\$8$ each, respectively. What is the largest number of mogs he can purchase if he must buy at least one of each item and will spend exactly $\$100$? | 10 | <｜begin▁of▁sentence｜><｜User｜>Bill can buy mags, migs, and mogs for $\$3$, $\$4$, and $\$8$ each, respectively. What is the largest number of mogs he can purchase if he must buy at least one of each item and will spend exactly $\$100$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><th... | <think>
Okay, so I have this problem where Bill wants to buy mags, migs, and mogs. Each mag costs $3, each mig costs $4, and each mog costs $8. He wants to spend exactly $100, and he must buy at least one of each item. The question is asking for the largest number of mogs he can purchase under these conditions.
Hmm, l... | official | v4_conceptual | 14,976 | 3,779 | ba3ba61afaa76d06 | 10 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bill can buy mags, migs, and mogs for $\\$3$, $\\$4$, and $\\$8$ each, respectively. What is the largest number of mogs he can purchase if he must buy at least one of each item a... | 3,792 |
<｜begin▁of▁sentence｜><｜User｜>There are four distinct positive integers $a,b,c,d$ less than $8$ which are invertible modulo $8$. Find the remainder when $(abc+abd+acd+bcd)(abcd)^{-1}$ is divided by $8$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, let's try to so... | deepscaler_teacher_vllm_clean_v4_conceptual | math | There are four distinct positive integers $a,b,c,d$ less than $8$ which are invertible modulo $8$. Find the remainder when $(abc+abd+acd+bcd)(abcd)^{-1}$ is divided by $8$. | 0 | <｜begin▁of▁sentence｜><｜User｜>There are four distinct positive integers $a,b,c,d$ less than $8$ which are invertible modulo $8$. Find the remainder when $(abc+abd+acd+bcd)(abcd)^{-1}$ is divided by $8$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, let's try to solve this problem step by step. The problem is about four distinct positive integers a, b, c, d less than 8, which are invertible modulo 8. We need to find the remainder when (abc + abd + acd + bcd)(abcd)^{-1} is divided by 8.
First, let me understand what it means for a number to be invert... | official | v4_conceptual | 18,812 | 3,581 | 48c7711cb1df5417 | 0 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are four distinct positive integers $a,b,c,d$ less than $8$ which are invertible modulo $8$. Find the remainder when $(abc+abd+acd+bcd)(abcd)^{-1}$ is divided by $8$.",
... | 3,594 |
<｜begin▁of▁sentence｜><｜User｜>Throw a fair die, and let event $A$ be that the number facing up is even, and event $B$ be that the number facing up is greater than $2$ and less than or equal to $5$. Then, the probability of the complement of event $B$ is ____, and the probability of event $A \cup B$ is $P(A \cup B) = $ _... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Throw a fair die, and let event $A$ be that the number facing up is even, and event $B$ be that the number facing up is greater than $2$ and less than or equal to $5$. Then, the probability of the complement of event $B$ is ____, and the probability of event $A \cup B$ is $P(A \cup B) = $ ____. | \dfrac{5}{6} | <｜begin▁of▁sentence｜><｜User｜>Throw a fair die, and let event $A$ be that the number facing up is even, and event $B$ be that the number facing up is greater than $2$ and less than or equal to $5$. Then, the probability of the complement of event $B$ is ____, and the probability of event $A \cup B$ is $P(A \cup B) = $ _... | <think>
Okay, so I have this problem where I need to find two probabilities: the probability of the complement of event B, and the probability of event A union B. Let me try to break this down step by step.
First, let's understand the problem. We're dealing with a fair die. A fair die has six faces, numbered 1 through... | official | v4_conceptual | 9,664 | 1,623 | 0401633ae91f692c | \dfrac{5}{6} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Throw a fair die, and let event $A$ be that the number facing up is even, and event $B$ be that the number facing up is greater than $2$ and less than or equal to $5$. Then, the ... | 1,636 |
<｜begin▁of▁sentence｜><｜User｜>What two digits should be added to the right of the number 2013, so that the resulting six-digit number is divisible by 101? Find all possible solutions. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out what two d... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What two digits should be added to the right of the number 2013, so that the resulting six-digit number is divisible by 101? Find all possible solutions. | 94 | <｜begin▁of▁sentence｜><｜User｜>What two digits should be added to the right of the number 2013, so that the resulting six-digit number is divisible by 101? Find all possible solutions. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out what two digits should be added to the right of the number 2013 to make it a six-digit number divisible by 101. Hmm, let's break this down step by step.
First, let me understand the problem. The number given is 2013, and we need to add two digits to the right. So, the resulting nu... | official | v4_conceptual | 7,527 | 2,803 | f33411383a93590d | 94 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What two digits should be added to the right of the number 2013, so that the resulting six-digit number is divisible by 101? Find all possible solutions.",
"role": "user"
}... | 2,816 |
<｜begin▁of▁sentence｜><｜User｜>Three male students and two female students stand in a row. The total number of arrangements where the female students do not stand at the ends is given by what total count. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Three male students and two female students stand in a row. The total number of arrangements where the female students do not stand at the ends is given by what total count. | 36 | <｜begin▁of▁sentence｜><｜User｜>Three male students and two female students stand in a row. The total number of arrangements where the female students do not stand at the ends is given by what total count. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: there are three male students and two female students standing in a row. I need to find the total number of arrangements where the female students do not stand at the ends. Hmm, let me try to figure this out step by step.
First, let me understand the problem. There are a total of ... | official | v4_conceptual | 29,142 | 3,265 | 0157489af39eee7e | 36 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three male students and two female students stand in a row. The total number of arrangements where the female students do not stand at the ends is given by what total count.",
... | 3,278 |
<｜begin▁of▁sentence｜><｜User｜>When a certain unfair die is rolled, an even number is $5$ times as likely to appear as an odd number. The die is rolled twice. Calculate the probability that the sum of the numbers rolled is odd. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><thin... | deepscaler_teacher_vllm_clean_v4_conceptual | math | When a certain unfair die is rolled, an even number is $5$ times as likely to appear as an odd number. The die is rolled twice. Calculate the probability that the sum of the numbers rolled is odd. | \frac{5}{18} | <｜begin▁of▁sentence｜><｜User｜>When a certain unfair die is rolled, an even number is $5$ times as likely to appear as an odd number. The die is rolled twice. Calculate the probability that the sum of the numbers rolled is odd. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem about an unfair die. Let me try to understand it step by step. The problem says that when this die is rolled, an even number is 5 times as likely to appear as an odd number. Then, it's rolled twice, and we need to find the probability that the sum of the numbers rolled is odd. Hmm, ... | official | v4_conceptual | 33,806 | 2,948 | a920e5b52ced22ff | \dfrac{5}{18} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When a certain unfair die is rolled, an even number is $5$ times as likely to appear as an odd number. The die is rolled twice. Calculate the probability that the sum of the numb... | 2,961 |
<｜begin▁of▁sentence｜><｜User｜>Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower? Let's think step by step and ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower? | 0.4 | <｜begin▁of▁sentence｜><｜User｜>Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower? Let's think step by step and ... | <think>
Okay, so Logan is building a scaled model of his town, and he needs to figure out the height of the miniature water tower. The real water tower is 40 meters high, and it has a spherical top that holds 100,000 liters of water. The miniature holds 0.1 liters. Hmm, so I think this is a scaling problem where the vo... | official | v4_conceptual | 20,198 | 2,051 | 6ab7c7e8b2108df0 | 0.4 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniat... | 2,064 |
<｜begin▁of▁sentence｜><｜User｜>Given the ellipse C: $$\frac {x^{2}}{25}+ \frac {y^{2}}{9}=1$$, F is the right focus, and l is a line passing through point F (not parallel to the y-axis), intersecting the ellipse at points A and B. l′ is the perpendicular bisector of AB, intersecting the major axis of the ellipse at point... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the ellipse C: $$\frac {x^{2}}{25}+ \frac {y^{2}}{9}=1$$, F is the right focus, and l is a line passing through point F (not parallel to the y-axis), intersecting the ellipse at points A and B. l′ is the perpendicular bisector of AB, intersecting the major axis of the ellipse at point D. Then the value of $$\frac... | \frac {2}{5} | <｜begin▁of▁sentence｜><｜User｜>Given the ellipse C: $$\frac {x^{2}}{25}+ \frac {y^{2}}{9}=1$$, F is the right focus, and l is a line passing through point F (not parallel to the y-axis), intersecting the ellipse at points A and B. l′ is the perpendicular bisector of AB, intersecting the major axis of the ellipse at point... | <think>
Okay, so I have this problem about an ellipse, and I need to find the value of DF divided by AB. Let's break it down step by step.
First, the ellipse is given by the equation x²/25 + y²/9 = 1. That means it's an ellipse centered at the origin, with semi-major axis a=5 and semi-minor axis b=3. Since a > b, the ... | official | v4_conceptual | 35,648 | 3,402 | 32010745c11d3a8f | \dfrac{2}{5} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the ellipse C: $$\\frac {x^{2}}{25}+ \\frac {y^{2}}{9}=1$$, F is the right focus, and l is a line passing through point F (not parallel to the y-axis), intersecting the ell... | 3,415 |
<｜begin▁of▁sentence｜><｜User｜>Bryan has some 3 cent stamps and some 4 cent stamps. What is the least number of stamps he can combine so the value of the stamps is 33 cents? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so Bryan has some 3-cent stamps and some 4-ce... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Bryan has some 3 cent stamps and some 4 cent stamps. What is the least number of stamps he can combine so the value of the stamps is 33 cents? | 9 | <｜begin▁of▁sentence｜><｜User｜>Bryan has some 3 cent stamps and some 4 cent stamps. What is the least number of stamps he can combine so the value of the stamps is 33 cents? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so Bryan has some 3-cent stamps and some 4-cent stamps. He wants to combine them in such a way that the total value is 33 cents, and we need to find the least number of stamps he can use. Hmm, let's try to figure this out step by step.
First, let's define the variables. Let me denote the number of 3-cent... | official | v4_conceptual | 18,790 | 1,572 | d1263875d1734abc | 9 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bryan has some 3 cent stamps and some 4 cent stamps. What is the least number of stamps he can combine so the value of the stamps is 33 cents?",
"role": "user"
},
{
"... | 1,585 |
<｜begin▁of▁sentence｜><｜User｜>How many whole numbers are between $\sqrt{8}$ and $\sqrt{80}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: "How many whole numbers are between sqrt(8) and sqrt(80)." Hmm, let me try to figure this out step by... | deepscaler_teacher_vllm_clean_v4_conceptual | math | How many whole numbers are between $\sqrt{8}$ and $\sqrt{80}$? | 6 | <｜begin▁of▁sentence｜><｜User｜>How many whole numbers are between $\sqrt{8}$ and $\sqrt{80}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: "How many whole numbers are between sqrt(8) and sqrt(80)." Hmm, let me try to figure this out step by step.
First, I need to understand what exactly the question is asking. It's about whole numbers lying between the square roots of 8 and 80. So, I think I need to find all the whol... | official | v4_conceptual | 807 | 1,923 | a1a47747b9cf7ed8 | 6 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many whole numbers are between $\\sqrt{8}$ and $\\sqrt{80}$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem: \"How many whole numbers are... | 1,936 |
<｜begin▁of▁sentence｜><｜User｜>Express $326_{13} + 4C9_{14}$ as a base 10 integer, where $C = 12$ in base 14. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem where I need to add two numbers from different bases and express the result in base 10... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Express $326_{13} + 4C9_{14}$ as a base 10 integer, where $C = 12$ in base 14. | 1500 | <｜begin▁of▁sentence｜><｜User｜>Express $326_{13} + 4C9_{14}$ as a base 10 integer, where $C = 12$ in base 14. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to add two numbers from different bases and express the result in base 10. The numbers are given as \(326_{13}\) and \(4C9_{14}\), and I know that \(C = 12\) in base 14. Hmm, let's break this down step by step.
First, I need to understand each number separately. The fi... | official | v4_conceptual | 31,510 | 1,819 | c0923a3d215648bb | 1500 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Express $326_{13} + 4C9_{14}$ as a base 10 integer, where $C = 12$ in base 14.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem where I need to... | 1,832 |
<｜begin▁of▁sentence｜><｜User｜>Let $f(x)$ have a derivative, and satisfy $\lim_{\Delta x \to 0} \frac{f(1)-f(1-2\Delta x)}{2\Delta x}=-1$. Find the slope of the tangent line at point $(1,f(1))$ on the curve $y=f(x)$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let $f(x)$ have a derivative, and satisfy $\lim_{\Delta x \to 0} \frac{f(1)-f(1-2\Delta x)}{2\Delta x}=-1$. Find the slope of the tangent line at point $(1,f(1))$ on the curve $y=f(x)$. | -1 | <｜begin▁of▁sentence｜><｜User｜>Let $f(x)$ have a derivative, and satisfy $\lim_{\Delta x \to 0} \frac{f(1)-f(1-2\Delta x)}{2\Delta x}=-1$. Find the slope of the tangent line at point $(1,f(1))$ on the curve $y=f(x)$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to find the slope of the tangent line to the curve y = f(x) at the point (1, f(1)). The given information is that the limit as Δx approaches 0 of [f(1) - f(1 - 2Δx)] divided by (2Δx) is equal to -1. Hmm, let's try to parse this step by step.
First, I know that the defi... | official | v4_conceptual | 25,419 | 3,261 | d0376d658269b100 | -1 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ have a derivative, and satisfy $\\lim_{\\Delta x \\to 0} \\frac{f(1)-f(1-2\\Delta x)}{2\\Delta x}=-1$. Find the slope of the tangent line at point $(1,f(1))$ on the cu... | 3,274 |
<｜begin▁of▁sentence｜><｜User｜>What is the sum of the distinct prime integer divisors of $2016$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the sum of the distinct prime integer divisors of 2016. Hmm, let's start by understanding what the probl... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the sum of the distinct prime integer divisors of $2016$? | 12 | <｜begin▁of▁sentence｜><｜User｜>What is the sum of the distinct prime integer divisors of $2016$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the sum of the distinct prime integer divisors of 2016. Hmm, let's start by understanding what the problem is asking. It wants the sum of all the different prime numbers that can divide 2016 without leaving a remainder. So, first, I should probably factorize 2016 into its prime factors a... | official | v4_conceptual | 21,554 | 1,330 | 3847b4e1709816dd | 12 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of the distinct prime integer divisors of $2016$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the sum of the distinct prime int... | 1,343 |
<｜begin▁of▁sentence｜><｜User｜>How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out how many ways there are to put 7 distinguishable balls int... | deepscaler_teacher_vllm_clean_v4_conceptual | math | How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not? | 64 | <｜begin▁of▁sentence｜><｜User｜>How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out how many ways there are to put 7 distinguishable balls into 2 indistinguishable boxes. Hmm, let me think about this step by step.
First, I remember that when dealing with distinguishable objects and distinguishable boxes, the number of ways is straightforward because each object c... | official | v4_conceptual | 30,802 | 3,435 | bdbc8471a876083c | 64 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need t... | 3,448 |
<｜begin▁of▁sentence｜><｜User｜>Let $M_n$ be the $n \times n$ matrix with entries as follows: for $1 \le i \le n$, $m_{i,i} = 10$; for $1 \le i \le n - 1$, $m_{i+1,i} = m_{i,i+1} = 3$; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$. Then $\sum_{n=1}^{\infty} \frac{1}{8D_n+1}$ can be repr... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let $M_n$ be the $n \times n$ matrix with entries as follows: for $1 \le i \le n$, $m_{i,i} = 10$; for $1 \le i \le n - 1$, $m_{i+1,i} = m_{i,i+1} = 3$; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$. Then $\sum_{n=1}^{\infty} \frac{1}{8D_n+1}$ can be represented as $\frac{p}{q}$, whe... | 73 | <｜begin▁of▁sentence｜><｜User｜>Let $M_n$ be the $n \times n$ matrix with entries as follows: for $1 \le i \le n$, $m_{i,i} = 10$; for $1 \le i \le n - 1$, $m_{i+1,i} = m_{i,i+1} = 3$; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$. Then $\sum_{n=1}^{\infty} \frac{1}{8D_n+1}$ can be repr... | <think>
Okay, so I have this problem about determinants of a specific type of matrix and then summing a series based on those determinants. Let me try to break it down step by step.
First, let me understand the matrix M_n. It's an n x n matrix where the diagonal entries are all 10, the entries immediately above and be... | official | v4_conceptual | 3,513 | 3,586 | ea56f044397c345a | 73 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $M_n$ be the $n \\times n$ matrix with entries as follows: for $1 \\le i \\le n$, $m_{i,i} = 10$; for $1 \\le i \\le n - 1$, $m_{i+1,i} = m_{i,i+1} = 3$; all other entries in... | 3,599 |
<｜begin▁of▁sentence｜><｜User｜>Given that $f: x \rightarrow \sqrt{x}$ is a function from set $A$ to set $B$.
1. If $A=[0,9]$, then the range of the function $f(x)$ is ________.
2. If $B={1,2}$, then $A \cap B =$ ________. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Oka... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given that $f: x \rightarrow \sqrt{x}$ is a function from set $A$ to set $B$.
1. If $A=[0,9]$, then the range of the function $f(x)$ is ________.
2. If $B={1,2}$, then $A \cap B =$ ________. | {1} | <｜begin▁of▁sentence｜><｜User｜>Given that $f: x \rightarrow \sqrt{x}$ is a function from set $A$ to set $B$.
1. If $A=[0,9]$, then the range of the function $f(x)$ is ________.
2. If $B={1,2}$, then $A \cap B =$ ________. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this function f: x → √x, which is a function from set A to set B. There are two parts to this problem. Let me tackle them one by one.
Starting with the first question: If A is [0,9], then what is the range of the function f(x) = √x?
Alright, so f(x) is the square root of x. Since the domain A ... | official | v4_conceptual | 28,554 | 2,179 | 9c3b09a05ac82866 | \{1\} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $f: x \\rightarrow \\sqrt{x}$ is a function from set $A$ to set $B$.\n1. If $A=[0,9]$, then the range of the function $f(x)$ is ________.\n2. If $B={1,2}$, then $A \\c... | 2,192 |
<｜begin▁of▁sentence｜><｜User｜>Given the sequence 1, 1+2, 2+3+4, 3+4+5+6, ..., find the value of the 8th term. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the 8th term of this sequence: 1, 1+2, 2+3+4, 3+4+5+6, and so on. Hmm, let me try to under... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the sequence 1, 1+2, 2+3+4, 3+4+5+6, ..., find the value of the 8th term. | 84 | <｜begin▁of▁sentence｜><｜User｜>Given the sequence 1, 1+2, 2+3+4, 3+4+5+6, ..., find the value of the 8th term. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the 8th term of this sequence: 1, 1+2, 2+3+4, 3+4+5+6, and so on. Hmm, let me try to understand the pattern here.
First, let's write down the given terms:
1st term: 1
2nd term: 1 + 2
3rd term: 2 + 3 + 4
4th term: 3 + 4 + 5 + 6
Wait, hold on. Let me check if that's correct. The firs... | official | v4_conceptual | 29,294 | 3,635 | bd37a181fb9c3d98 | 84 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence 1, 1+2, 2+3+4, 3+4+5+6, ..., find the value of the 8th term.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the 8th term of thi... | 3,648 |
<｜begin▁of▁sentence｜><｜User｜>The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octahedral dice? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Oka... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octahedral dice? | \frac{1}{32} | <｜begin▁of▁sentence｜><｜User｜>The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octahedral dice? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the probability of rolling a sum of 15 with a pair of octahedral dice, each labeled from 1 to 8. Hmm, let me break this down step by step.
First, I know that an octahedral die has 8 faces, so each die has numbers from 1 to 8. When rolling two such dice, the total number of possible outc... | official | v4_conceptual | 17,367 | 1,911 | 679110693e83ca73 | \dfrac{1}{32} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octa... | 1,924 |
<｜begin▁of▁sentence｜><｜User｜>"In a tree with black pearls hidden, this item is only available in May. Travelers who pass by taste one, with a mouthful of sweetness and sourness, never wanting to leave." The Dongkui waxberry is a sweet gift in summer. Each batch of Dongkui waxberries must undergo two rounds of testing b... | deepscaler_teacher_vllm_clean_v4_conceptual | math | "In a tree with black pearls hidden, this item is only available in May. Travelers who pass by taste one, with a mouthful of sweetness and sourness, never wanting to leave." The Dongkui waxberry is a sweet gift in summer. Each batch of Dongkui waxberries must undergo two rounds of testing before entering the market. Th... | 640 | <｜begin▁of▁sentence｜><｜User｜>"In a tree with black pearls hidden, this item is only available in May. Travelers who pass by taste one, with a mouthful of sweetness and sourness, never wanting to leave." The Dongkui waxberry is a sweet gift in summer. Each batch of Dongkui waxberries must undergo two rounds of testing b... | <think>
Okay, so I have this problem about Dongkui waxberries and their testing process. There are two parts: first, finding the probability that a batch cannot be sold, and second, dealing with the profit distribution for 4 batches. Let me tackle them one by one.
Starting with part (1): Find the probability that a ba... | official | v4_conceptual | 11,205 | 4,025 | 86a79ac09bdf9a02 | 640 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\"In a tree with black pearls hidden, this item is only available in May. Travelers who pass by taste one, with a mouthful of sweetness and sourness, never wanting to leave.\" Th... | 4,038 |
<｜begin▁of▁sentence｜><｜User｜>You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done.
Note: A regular dodecahedron has twelve pentagonal faces and in each vertex concur three edges. Th... | deepscaler_teacher_vllm_clean_v4_conceptual | math | You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done.
Note: A regular dodecahedron has twelve pentagonal faces and in each vertex concur three edges. The edges of the dodecahedron a... | 2048 | <｜begin▁of▁sentence｜><｜User｜>You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done.
Note: A regular dodecahedron has twelve pentagonal faces and in each vertex concur three edges. Th... | <think>
Okay, so I have this problem about a regular dodecahedron, which has 12 pentagonal faces and each vertex where three edges meet. The task is to determine the number of ways to paint some edges red such that each face has an even number of painted edges. The note says that edges are all different, so maybe it's ... | official | v4_conceptual | 28,817 | 2,634 | 986006ef18b52d95 | 2048 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration... | 2,647 |
<｜begin▁of▁sentence｜><｜User｜>Calculate the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition that are divisible by 9. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: I need to find the num... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Calculate the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition that are divisible by 9. | 16 | <｜begin▁of▁sentence｜><｜User｜>Calculate the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition that are divisible by 9. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: I need to find the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition, and these numbers should be divisible by 9. Hmm, let me think about how to approach this.
First, I remember that a number is divisible by 9 if the sum of its ... | official | v4_conceptual | 25,248 | 2,806 | 64ba6cef4eb7f79e | 16 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition that are divisible by 9.",
"role": "user"
},
{
"c... | 2,819 |
<｜begin▁of▁sentence｜><｜User｜>Let \{a_{n}\}_{n \geq 1}$ be an arithmetic sequence and \{g_{n}\}_{n \geq 1}$ be a geometric sequence such that the first four terms of \{a_{n}+g_{n}\}$ are $0,0,1$, and 0 , in that order. What is the 10th term of \{a_{n}+g_{n}\}$ ? Let's think step by step and output the final answer withi... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let \{a_{n}\}_{n \geq 1}$ be an arithmetic sequence and \{g_{n}\}_{n \geq 1}$ be a geometric sequence such that the first four terms of \{a_{n}+g_{n}\}$ are $0,0,1$, and 0 , in that order. What is the 10th term of \{a_{n}+g_{n}\}$ ? | -54 | <｜begin▁of▁sentence｜><｜User｜>Let \{a_{n}\}_{n \geq 1}$ be an arithmetic sequence and \{g_{n}\}_{n \geq 1}$ be a geometric sequence such that the first four terms of \{a_{n}+g_{n}\}$ are $0,0,1$, and 0 , in that order. What is the 10th term of \{a_{n}+g_{n}\}$ ? Let's think step by step and output the final answer withi... | <think>
Okay, so I have this problem where there's an arithmetic sequence {a_n} and a geometric sequence {g_n}. The first four terms of the sequence {a_n + g_n} are given as 0, 0, 1, 0. I need to find the 10th term of {a_n + g_n}.
First, let's recall what an arithmetic sequence is. An arithmetic sequence has a common ... | official | v4_conceptual | 2,093 | 3,609 | c97227e5629f5e68 | -54 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\{a_{n}\\}_{n \\geq 1}$ be an arithmetic sequence and \\{g_{n}\\}_{n \\geq 1}$ be a geometric sequence such that the first four terms of \\{a_{n}+g_{n}\\}$ are $0,0,1$, and ... | 3,622 |
<｜begin▁of▁sentence｜><｜User｜>Given that vectors $a$ and $b$ satisfy $(2a+3b) \perp b$, and $|b|=2\sqrt{2}$, find the projection of vector $a$ onto the direction of $b$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: vectors a and b sat... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given that vectors $a$ and $b$ satisfy $(2a+3b) \perp b$, and $|b|=2\sqrt{2}$, find the projection of vector $a$ onto the direction of $b$. | -3\sqrt{2} | <｜begin▁of▁sentence｜><｜User｜>Given that vectors $a$ and $b$ satisfy $(2a+3b) \perp b$, and $|b|=2\sqrt{2}$, find the projection of vector $a$ onto the direction of $b$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: vectors a and b satisfy (2a + 3b) is perpendicular to b, and the magnitude of b is 2√2. I need to find the projection of vector a onto the direction of b. Hmm, let me think about how to approach this.
First, let's recall what it means for two vectors to be perpendicular. If t... | official | v4_conceptual | 5,462 | 3,360 | 4c4e0e9593e14bfd | -3\sqrt{2} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that vectors $a$ and $b$ satisfy $(2a+3b) \\perp b$, and $|b|=2\\sqrt{2}$, find the projection of vector $a$ onto the direction of $b$.",
"role": "user"
},
{
"c... | 3,373 |
<｜begin▁of▁sentence｜><｜User｜>A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I've got this problem her... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle? | 50 | <｜begin▁of▁sentence｜><｜User｜>A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I've got this problem here. Let me read it again: A square has an area of 25. A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle? Hmm, okay.
Alright, let me break this down. First, it's talking about a square with area 25. I... | official | v4_conceptual | 39,656 | 1,085 | 198bdfd332fc357c | 50 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle?",
"role": "use... | 1,098 |
<｜begin▁of▁sentence｜><｜User｜>The maximum value of $k$ such that the inequality $\sqrt{x-3}+\sqrt{6-x}\geq k$ has a real solution. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this inequality: √(x - 3) + √(6 - x) ≥ k. I need to find the maximum valu... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The maximum value of $k$ such that the inequality $\sqrt{x-3}+\sqrt{6-x}\geq k$ has a real solution. | \sqrt{6} | <｜begin▁of▁sentence｜><｜User｜>The maximum value of $k$ such that the inequality $\sqrt{x-3}+\sqrt{6-x}\geq k$ has a real solution. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this inequality: √(x - 3) + √(6 - x) ≥ k. I need to find the maximum value of k such that this inequality has a real solution. Hmm, let's break this down step by step.
First, I should figure out the domain of this inequality because we have square roots. For √(x - 3) to be real, x - 3 must be ≥... | official | v4_conceptual | 31,768 | 1,868 | c0cb09a45b161d94 | \sqrt{6} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The maximum value of $k$ such that the inequality $\\sqrt{x-3}+\\sqrt{6-x}\\geq k$ has a real solution.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have... | 1,881 |
<｜begin▁of▁sentence｜><｜User｜>Calculate the value of the expression $2+3 imes 5+2$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this math problem here: Calculate the value of the expression 2 + 3 × 5 + 2. Hmm, let me see how to approach this. I rememb... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Calculate the value of the expression $2+3 imes 5+2$. | 19 | <｜begin▁of▁sentence｜><｜User｜>Calculate the value of the expression $2+3 imes 5+2$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this math problem here: Calculate the value of the expression 2 + 3 × 5 + 2. Hmm, let me see how to approach this. I remember from school that when solving math problems, especially expressions with multiple operations, I need to follow the order of operations. I think it's often remembered by t... | official | v4_conceptual | 2,760 | 907 | 9d954b8418af5423 | 19 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the expression $2+3 \times 5+2$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this math problem here: Calculate the value of the ... | 920 |
<｜begin▁of▁sentence｜><｜User｜>A rectangle is called cool if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths. What is the sum of all the different possible areas of cool rectangles? Let's think step by step and output the ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A rectangle is called cool if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths. What is the sum of all the different possible areas of cool rectangles? | 236 | <｜begin▁of▁sentence｜><｜User｜>A rectangle is called cool if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths. What is the sum of all the different possible areas of cool rectangles? Let's think step by step and output the ... | <think>
Okay, so I have this problem about a "cool" rectangle. Let me first understand what it's asking. A rectangle is cool if its area is equal to twice its perimeter. Also, the side lengths must be integers. I need to find all such rectangles and then sum up all their different areas.
Alright, let's break it down. ... | official | v4_conceptual | 37,447 | 1,768 | 8e5abe6e0541c115 | 236 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle is called cool if the number of square units in its area is equal to twice the number of units in its perimeter. A cool rectangle also must have integer side lengths.... | 1,781 |
<｜begin▁of▁sentence｜><｜User｜>The remainder can be defined for all real numbers $x$ and $y$ with $y \neq 0$ by $\text{rem} (x ,y)=x-y\left \lfloor \frac{x}{y} \right \rfloor$ where $\left \lfloor \tfrac{x}{y} \right \rfloor$ denotes the greatest integer less than or equal to $\tfrac{x}{y}$. What is the value of $\text{r... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The remainder can be defined for all real numbers $x$ and $y$ with $y \neq 0$ by $\text{rem} (x ,y)=x-y\left \lfloor \frac{x}{y} \right \rfloor$ where $\left \lfloor \tfrac{x}{y} \right \rfloor$ denotes the greatest integer less than or equal to $\tfrac{x}{y}$. What is the value of $\text{rem} (\tfrac{3}{8}, -\tfrac{2}... | -\frac{1}{40} | <｜begin▁of▁sentence｜><｜User｜>The remainder can be defined for all real numbers $x$ and $y$ with $y \neq 0$ by $\text{rem} (x ,y)=x-y\left \lfloor \frac{x}{y} \right \rfloor$ where $\left \lfloor \tfrac{x}{y} \right \rfloor$ denotes the greatest integer less than or equal to $\tfrac{x}{y}$. What is the value of $\text{r... | <think>
Okay, so I have this problem where I need to find the remainder when dividing 3/8 by -2/5 using the definition of remainder provided. The formula is rem(x, y) = x - y * floor(x/y). Hmm, let me break this down step by step.
First, let's identify x and y. Here, x is 3/8 and y is -2/5. So, x = 3/8 and y = -2/5.
... | official | v4_conceptual | 20,581 | 2,888 | d445baaa0e2f43f9 | -\dfrac{1}{40} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The remainder can be defined for all real numbers $x$ and $y$ with $y \\neq 0$ by $\\text{rem} (x ,y)=x-y\\left \\lfloor \\frac{x}{y} \\right \\rfloor$ where $\\left \\lfloor \\t... | 2,901 |
<｜begin▁of▁sentence｜><｜User｜>What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{2310}$ is defined? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the smallest integer n, greater than 1, such that n inverse modulo 2310 is d... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{2310}$ is defined? | 13 | <｜begin▁of▁sentence｜><｜User｜>What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{2310}$ is defined? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the smallest integer n, greater than 1, such that n inverse modulo 2310 is defined. Hmm, let's break this down.
First, I remember that the inverse of n modulo m exists if and only if n and m are coprime, meaning their greatest common divisor (gcd) is 1. So, in this case, m is 2310. The... | official | v4_conceptual | 8,677 | 1,252 | 1ef172247cd44060 | 13 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest integer $n$, greater than $1$, such that $n^{-1}\\pmod{2310}$ is defined?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the ... | 1,265 |
<｜begin▁of▁sentence｜><｜User｜>Two students, A and B, each select two courses from four elective courses. The probability that they share exactly one course in common is ______. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I've got this probability problem here... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Two students, A and B, each select two courses from four elective courses. The probability that they share exactly one course in common is ______. | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Two students, A and B, each select two courses from four elective courses. The probability that they share exactly one course in common is ______. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I've got this probability problem here. Let me read it again:
"Two students, A and B, each select two courses from four elective courses. The probability that they share exactly one course in common is ______. Let's think step by step and output the final answer within \boxed{}."
Alright, so we have ... | official | v4_conceptual | 28,538 | 3,089 | f511eb1c590a2f3d | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two students, A and B, each select two courses from four elective courses. The probability that they share exactly one course in common is ______.",
"role": "user"
},
{
... | 3,102 |
<｜begin▁of▁sentence｜><｜User｜>The product of all the positive integer divisors of \( 6^{16} \) equals \( 6^k \) for some integer \( k \). Determine the value of \( k \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: The product of all the p... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The product of all the positive integer divisors of \( 6^{16} \) equals \( 6^k \) for some integer \( k \). Determine the value of \( k \). | 2312 | <｜begin▁of▁sentence｜><｜User｜>The product of all the positive integer divisors of \( 6^{16} \) equals \( 6^k \) for some integer \( k \). Determine the value of \( k \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: The product of all the positive integer divisors of \(6^{16}\) equals \(6^k\) for some integer \(k\). I need to find the value of \(k\). Hmm, let's break this down step by step.
First, I remember that for any number, the product of its divisors can be found using a formula. I thin... | official | v4_conceptual | 4,335 | 2,912 | 018fff719f9abcd1 | 2312 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The product of all the positive integer divisors of \\( 6^{16} \\) equals \\( 6^k \\) for some integer \\( k \\). Determine the value of \\( k \\).",
"role": "user"
},
{
... | 2,925 |
<｜begin▁of▁sentence｜><｜User｜>Given an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ($a>0$, $b>0$) with its left focus $F$ and right vertex $A$, upper vertex $B$. If the distance from point $F$ to line $AB$ is $\frac{5\sqrt{14}}{14}b$, find the eccentricity of the ellipse. Let's think step by step and output ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ($a>0$, $b>0$) with its left focus $F$ and right vertex $A$, upper vertex $B$. If the distance from point $F$ to line $AB$ is $\frac{5\sqrt{14}}{14}b$, find the eccentricity of the ellipse. | \frac{2}{3} | <｜begin▁of▁sentence｜><｜User｜>Given an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ($a>0$, $b>0$) with its left focus $F$ and right vertex $A$, upper vertex $B$. If the distance from point $F$ to line $AB$ is $\frac{5\sqrt{14}}{14}b$, find the eccentricity of the ellipse. Let's think step by step and output ... | <think>
Okay, so I have this problem about an ellipse, and I need to find its eccentricity. Let me try to break it down step by step.
First, the equation of the ellipse is given as (x²/a²) + (y²/b²) = 1, where a and b are positive. I remember that in an ellipse, a is the semi-major axis and b is the semi-minor axis. B... | official | v4_conceptual | 36,619 | 3,803 | 7943ab526363e893 | \dfrac{2}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse $\\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1$ ($a>0$, $b>0$) with its left focus $F$ and right vertex $A$, upper vertex $B$. If the distance from point $F$ t... | 3,816 |
<｜begin▁of▁sentence｜><｜User｜>Sasha has $\$3.20$ in U.S. coins. She has the same number of quarters and nickels. What is the greatest number of quarters she could have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, let's see. So Sasha has $3.20 in U.S. coins. She ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Sasha has $\$3.20$ in U.S. coins. She has the same number of quarters and nickels. What is the greatest number of quarters she could have? | 10 | <｜begin▁of▁sentence｜><｜User｜>Sasha has $\$3.20$ in U.S. coins. She has the same number of quarters and nickels. What is the greatest number of quarters she could have? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, let's see. So Sasha has $3.20 in U.S. coins. She has the same number of quarters and nickels. We need to find the greatest number of quarters she could have. Hmm, okay.
First, let me note down what I know. She has quarters, nickels, and presumably other coins because the total is $3.20. Wait, the problem... | official | v4_conceptual | 39,684 | 2,138 | e7a9b470eb0014f3 | 10 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sasha has $\\$3.20$ in U.S. coins. She has the same number of quarters and nickels. What is the greatest number of quarters she could have?",
"role": "user"
},
{
"con... | 2,151 |
<｜begin▁of▁sentence｜><｜User｜>The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$ Find the vertex of the parabola $y = -x^2 + ax + b.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this inequality: y = -x² + a x ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$ Find the vertex of the parabola $y = -x^2 + ax + b.$ | (1,16) | <｜begin▁of▁sentence｜><｜User｜>The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$ Find the vertex of the parabola $y = -x^2 + ax + b.$ Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this inequality: y = -x² + a x + b ≤ 0, and the solution is given as (-∞, -3] ∪ [5, ∞). I need to find the vertex of the parabola y = -x² + a x + b.
First, let me recall that the inequality y ≤ 0 represents the region where the parabola is below or on the x-axis. The solution given is (-∞, -3] ... | official | v4_conceptual | 38,866 | 2,557 | c372be3b0a1f3508 | (1, 16) | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The solution to the inequality\n\\[y = -x^2 + ax + b \\le 0\\]is $(-\\infty,-3] \\cup [5,\\infty).$ Find the vertex of the parabola $y = -x^2 + ax + b.$",
"role": "user"
}... | 2,570 |
<｜begin▁of▁sentence｜><｜User｜>Two students are preparing to register for the independent admission tests of Zhejiang University, Fudan University, and Shanghai Jiao Tong University, with the requirement that each person can choose at most two schools. Calculate the number of different registration results. Let's think s... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Two students are preparing to register for the independent admission tests of Zhejiang University, Fudan University, and Shanghai Jiao Tong University, with the requirement that each person can choose at most two schools. Calculate the number of different registration results. | 36 | <｜begin▁of▁sentence｜><｜User｜>Two students are preparing to register for the independent admission tests of Zhejiang University, Fudan University, and Shanghai Jiao Tong University, with the requirement that each person can choose at most two schools. Calculate the number of different registration results. Let's think s... | <think>
Okay, so I need to figure out how many different registration results there are for two students when they can each choose at most two schools out of Zhejiang University, Fudan University, and Shanghai Jiao Tong University. Hmm, let's break this down step by step.
First, let me understand the problem. There ar... | official | v4_conceptual | 14,800 | 2,558 | d0fbcc88567d49d6 | 36 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two students are preparing to register for the independent admission tests of Zhejiang University, Fudan University, and Shanghai Jiao Tong University, with the requirement that ... | 2,571 |
<｜begin▁of▁sentence｜><｜User｜>Martians measure angles in clerts. There are $500$ clerts in a full circle. How many clerts are there in a right angle? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I'm trying to figure out how many clerts are in a right angle on ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Martians measure angles in clerts. There are $500$ clerts in a full circle. How many clerts are there in a right angle? | 125 | <｜begin▁of▁sentence｜><｜User｜>Martians measure angles in clerts. There are $500$ clerts in a full circle. How many clerts are there in a right angle? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I'm trying to figure out how many clerts are in a right angle on Mars. Martians measure angles in clerts, and it says there are 500 clerts in a full circle. Hmm, right angles... I remember that on Earth, a right angle is 90 degrees, which is a quarter of a full circle. So maybe on Mars, it's similar? L... | official | v4_conceptual | 434 | 971 | 4db79f7f9c21676d | 125 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Martians measure angles in clerts. There are $500$ clerts in a full circle. How many clerts are there in a right angle?",
"role": "user"
},
{
"content": "<think>\nOka... | 984 |
<｜begin▁of▁sentence｜><｜User｜>A designer has 3 fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color and one pattern, how many different dress designs are possible? Let's think step by step and output the final ans... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A designer has 3 fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color and one pattern, how many different dress designs are possible? | 12 | <｜begin▁of▁sentence｜><｜User｜>A designer has 3 fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color and one pattern, how many different dress designs are possible? Let's think step by step and output the final ans... | <think>
Okay, so I have this problem here about designing a dress. Let me try to figure it out step by step. The problem says there are 3 fabric colors: red, green, and blue. There are also 4 different patterns available for the dress. Each dress design needs exactly one color and one pattern. The question is asking ho... | official | v4_conceptual | 19,537 | 783 | b2d9c7229c52040f | 12 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A designer has 3 fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color ... | 796 |
<｜begin▁of▁sentence｜><｜User｜>Six consecutive numbers were written on a board. When one of them was crossed out and the remaining were summed, the result was 10085. What number could have been crossed out? Specify all possible options. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><th... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Six consecutive numbers were written on a board. When one of them was crossed out and the remaining were summed, the result was 10085. What number could have been crossed out? Specify all possible options. | 2020 | <｜begin▁of▁sentence｜><｜User｜>Six consecutive numbers were written on a board. When one of them was crossed out and the remaining were summed, the result was 10085. What number could have been crossed out? Specify all possible options. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><th... | <think>
Okay, so I have this problem here: six consecutive numbers were written on a board. When one of them was crossed out and the remaining were summed, the result was 10085. I need to figure out what number could have been crossed out. Hmm, let's see.
First, let's understand the problem. We have six consecutive nu... | official | v4_conceptual | 26,756 | 2,953 | 4c114d0ba2d3d801 | 2020 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six consecutive numbers were written on a board. When one of them was crossed out and the remaining were summed, the result was 10085. What number could have been crossed out? Sp... | 2,966 |
<｜begin▁of▁sentence｜><｜User｜>Let $m/n$, in lowest terms, be the probability that a randomly chosen positive divisor of $10^{99}$ is an integer multiple of $10^{88}$. Find $m + n$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: I need t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let $m/n$, in lowest terms, be the probability that a randomly chosen positive divisor of $10^{99}$ is an integer multiple of $10^{88}$. Find $m + n$. | 634 | <｜begin▁of▁sentence｜><｜User｜>Let $m/n$, in lowest terms, be the probability that a randomly chosen positive divisor of $10^{99}$ is an integer multiple of $10^{88}$. Find $m + n$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: I need to find the probability that a randomly chosen positive divisor of \(10^{99}\) is an integer multiple of \(10^{88}\). The answer should be expressed as a reduced fraction \( \frac{m}{n} \), and then I have to find \( m + n \). Hmm, let's break this down step by step.
F... | official | v4_conceptual | 23,396 | 2,181 | 4e2ccd546fa8f363 | 634 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $m/n$, in lowest terms, be the probability that a randomly chosen positive divisor of $10^{99}$ is an integer multiple of $10^{88}$. Find $m + n$.",
"role": "user"
},
... | 2,194 |
<｜begin▁of▁sentence｜><｜User｜>$A_{2n}^{n+3} + A_{4}^{n+1} = \boxed{\text{\_\_\_\_\_\_\_\_}}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: $A_{2n}^{n+3} + A_{4}^{n+1}$. Hmm, I think this notation refers to permutations. In combinatori... | deepscaler_teacher_vllm_clean_v4_conceptual | math | $A_{2n}^{n+3} + A_{4}^{n+1} = \boxed{\text{\_\_\_\_\_\_\_\_}}$. | 744 | <｜begin▁of▁sentence｜><｜User｜>$A_{2n}^{n+3} + A_{4}^{n+1} = \boxed{\text{\_\_\_\_\_\_\_\_}}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: $A_{2n}^{n+3} + A_{4}^{n+1}$. Hmm, I think this notation refers to permutations. In combinatorics, $A_k^m$ usually stands for the number of permutations of k items taken m at a time. So, that would be $P(k, m) = \frac{k!}{(k - m)!}$. Let me confirm that. Yeah, I think that's c... | official | v4_conceptual | 10,211 | 1,944 | 1991a5cf79561bdc | 744 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$A_{2n}^{n+3} + A_{4}^{n+1} = \\boxed{\\text{\\_\\_\\_\\_\\_\\_\\_\\_}}$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here: $A_{2n}^{n+3} ... | 1,957 |
<｜begin▁of▁sentence｜><｜User｜>In the equation $\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \frac {x}{m}$ the roots are equal when Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this equation here: (x(x - 1) - (m + 1)) / ((x - 1)(m - 1)) = x / m. I need t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In the equation $\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \frac {x}{m}$ the roots are equal when | -\frac{1}{2} | <｜begin▁of▁sentence｜><｜User｜>In the equation $\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \frac {x}{m}$ the roots are equal when Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this equation here: (x(x - 1) - (m + 1)) / ((x - 1)(m - 1)) = x / m. I need to find the value of m such that the roots are equal. Hmm, let's try to break this down step by step.
First, I should probably simplify both sides of the equation to make it easier to work with. Maybe cross-multiplying ... | official | v4_conceptual | 294 | 2,026 | b09edf59aa917bd5 | -\dfrac{1}{2} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the equation $\\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \\frac {x}{m}$ the roots are equal when",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this... | 2,039 |
<｜begin▁of▁sentence｜><｜User｜>Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225 pages, how many more minutes than Xanthia would it take for Molly to finish reading the book? Let's think step by step and output the final answer within \boxed{}.... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225 pages, how many more minutes than Xanthia would it take for Molly to finish reading the book? | 135 | <｜begin▁of▁sentence｜><｜User｜>Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225 pages, how many more minutes than Xanthia would it take for Molly to finish reading the book? Let's think step by step and output the final answer within \boxed{}.... | <think>
Okay, let's try to figure out how many more minutes it would take Molly to finish reading the book compared to Xanthia. Hmm, so first, both Xanthia and Molly are reading the same book, which has 225 pages. Xanthia can read 100 pages per hour, and Molly can read 50 pages per hour. I need to find the difference i... | official | v4_conceptual | 16,668 | 1,711 | 3af79a20254a9c8e | 135 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225 pages, how many more minutes than Xanthia would it... | 1,724 |
<｜begin▁of▁sentence｜><｜User｜>The volume of a regular triangular prism is $8$, the base edge length that minimizes the surface area of the prism is __________. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the base edge length that minimizes the ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The volume of a regular triangular prism is $8$, the base edge length that minimizes the surface area of the prism is __________. | 2\sqrt[3]{4} | <｜begin▁of▁sentence｜><｜User｜>The volume of a regular triangular prism is $8$, the base edge length that minimizes the surface area of the prism is __________. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the base edge length that minimizes the surface area of a regular triangular prism with a volume of 8. Hmm, let me try to break this down step by step.
First, let's recall what a regular triangular prism is. A regular triangular prism has two congruent equilateral triangles as its bases... | official | v4_conceptual | 10,328 | 3,510 | 6364ededa09d18f4 | 2\sqrt[3]{4} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The volume of a regular triangular prism is $8$, the base edge length that minimizes the surface area of the prism is __________.",
"role": "user"
},
{
"content": "<t... | 3,523 |
<｜begin▁of▁sentence｜><｜User｜>China Unicom charges for mobile phone calls with two types of packages: Package $A$ (monthly fee of $15$ yuan, call fee of $0.1 yuan per minute) and Package $B$ (monthly fee of $0$ yuan, call fee of $0.15 yuan per minute). Let $y_{1}$ represent the monthly bill for Package $A$ (in yuan), $y... | deepscaler_teacher_vllm_clean_v4_conceptual | math | China Unicom charges for mobile phone calls with two types of packages: Package $A$ (monthly fee of $15$ yuan, call fee of $0.1 yuan per minute) and Package $B$ (monthly fee of $0$ yuan, call fee of $0.15 yuan per minute). Let $y_{1}$ represent the monthly bill for Package $A$ (in yuan), $y_{2}$ represent the monthly b... | 300 | <｜begin▁of▁sentence｜><｜User｜>China Unicom charges for mobile phone calls with two types of packages: Package $A$ (monthly fee of $15$ yuan, call fee of $0.1 yuan per minute) and Package $B$ (monthly fee of $0$ yuan, call fee of $0.15 yuan per minute). Let $y_{1}$ represent the monthly bill for Package $A$ (in yuan), $y... | <think>
Okay, so I have this problem about Unicom's mobile phone packages. There are two packages, A and B. Let's break down what each part of the problem is asking.
First, part (1) says to express the functions of y₁ with respect to x and y₂ with respect to x. Hmm, so y₁ is the monthly bill for Package A, and y₂ is f... | official | v4_conceptual | 16,130 | 1,532 | fb6c1192f88ebb30 | 300 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "China Unicom charges for mobile phone calls with two types of packages: Package $A$ (monthly fee of $15$ yuan, call fee of $0.1 yuan per minute) and Package $B$ (monthly fee of $... | 1,545 |
<｜begin▁of▁sentence｜><｜User｜>Given that the line $y=x-2$ intersects the hyperbola $C: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a>0, b>0)$ at the intersection points $A$ and $B (not coincident)$. The perpendicular bisector of line segment $AB$ passes through the point $(4,0)$. The eccentricity of the hyperbola... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given that the line $y=x-2$ intersects the hyperbola $C: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a>0, b>0)$ at the intersection points $A$ and $B (not coincident)$. The perpendicular bisector of line segment $AB$ passes through the point $(4,0)$. The eccentricity of the hyperbola $C$ is ______. | \frac{2\sqrt{3}}{3} | <｜begin▁of▁sentence｜><｜User｜>Given that the line $y=x-2$ intersects the hyperbola $C: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a>0, b>0)$ at the intersection points $A$ and $B (not coincident)$. The perpendicular bisector of line segment $AB$ passes through the point $(4,0)$. The eccentricity of the hyperbola... | <think>
Okay, so I need to find the eccentricity of the hyperbola C given the conditions. Let me start by understanding the problem step by step.
First, the hyperbola is given by the equation \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) where \( a > 0 \) and \( b > 0 \). The line \( y = x - 2 \) intersects this hyperbo... | official | v4_conceptual | 15,855 | 3,088 | 8098524b34e66dc3 | \dfrac{2\sqrt{3}}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the line $y=x-2$ intersects the hyperbola $C: \\frac{{x}^{2}}{{a}^{2}}-\\frac{{y}^{2}}{{b}^{2}}=1 (a>0, b>0)$ at the intersection points $A$ and $B (not coincident)$. ... | 3,101 |
<｜begin▁of▁sentence｜><｜User｜>Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out the length of the trail Jitka hiked. The... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail? | 20 \text{ km} | <｜begin▁of▁sentence｜><｜User｜>Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out the length of the trail Jitka hiked. The problem says that after hiking 60% of the trail, she had 8 km left. Hmm, let me think step by step.
First, let me denote the total length of the trail as something. Maybe I'll call it L. So, the trail is L kilometers long.
Now, she hiked 6... | official | v4_conceptual | 22,842 | 791 | a1ad37ff32865549 | 20 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail?",
"role": "user"
},
{
"content": "<think>\... | 804 |
<｜begin▁of▁sentence｜><｜User｜>Compute the sum \[\lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \cdots + \lfloor \sqrt{25} \rfloor.\] Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to compute the sum of the floor of square... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Compute the sum \[\lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \cdots + \lfloor \sqrt{25} \rfloor.\] | 75 | <｜begin▁of▁sentence｜><｜User｜>Compute the sum \[\lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \cdots + \lfloor \sqrt{25} \rfloor.\] Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to compute the sum of the floor of square roots from 1 to 25. That is, I need to calculate:
\[
\lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \cdots + \lfloor \sqrt{25} \rfloor
\]
First, let me recall what the floor function does. The floor of a number is the ... | official | v4_conceptual | 12,099 | 3,589 | da47f3be51202836 | 75 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the sum \\[\\lfloor \\sqrt{1} \\rfloor + \\lfloor \\sqrt{2} \\rfloor + \\lfloor \\sqrt{3} \\rfloor + \\cdots + \\lfloor \\sqrt{25} \\rfloor.\\]",
"role": "user"
},
... | 3,602 |
<｜begin▁of▁sentence｜><｜User｜>A regular tetrahedron has an edge length of $2$. Calculate the surface area of the sphere circumscribed around this tetrahedron. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the surface area of the sphere that's cir... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A regular tetrahedron has an edge length of $2$. Calculate the surface area of the sphere circumscribed around this tetrahedron. | 6\pi | <｜begin▁of▁sentence｜><｜User｜>A regular tetrahedron has an edge length of $2$. Calculate the surface area of the sphere circumscribed around this tetrahedron. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the surface area of the sphere that's circumscribed around a regular tetrahedron with edge length 2. Hmm, let me break this down step by step.
First, I remember that a regular tetrahedron is a three-dimensional shape with four triangular faces, each of which is an equilateral triangle. ... | official | v4_conceptual | 24,236 | 2,877 | 4d9dacc51a3d8274 | 6\pi | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A regular tetrahedron has an edge length of $2$. Calculate the surface area of the sphere circumscribed around this tetrahedron.",
"role": "user"
},
{
"content": "<th... | 2,890 |
<｜begin▁of▁sentence｜><｜User｜>What is the minimum possible product of three different numbers of the set $\{-8,-6,-4,0,3,5,7\}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the minimum possible product of three different numbers from the set \{... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the minimum possible product of three different numbers of the set $\{-8,-6,-4,0,3,5,7\}$? | -280 | <｜begin▁of▁sentence｜><｜User｜>What is the minimum possible product of three different numbers of the set $\{-8,-6,-4,0,3,5,7\}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the minimum possible product of three different numbers from the set \{-8, -6, -4, 0, 3, 5, 7\}. Hmm, let me think about how to approach this.
First, I know that when looking for the minimum product, I need to consider both the largest negative numbers and the smallest positive numbers ... | official | v4_conceptual | 653 | 2,041 | 52472bcc18e1d422 | -280 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the minimum possible product of three different numbers of the set $\\{-8,-6,-4,0,3,5,7\\}$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to fin... | 2,054 |
<｜begin▁of▁sentence｜><｜User｜>Given that $|\vec{a}| = 1$ and $\vec{b} = (1, \sqrt{3})$, and that $(\vec{b} - \vec{a}) \perp \vec{a}$, find the angle between vector $\vec{a}$ and vector $\vec{b}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given that $|\vec{a}| = 1$ and $\vec{b} = (1, \sqrt{3})$, and that $(\vec{b} - \vec{a}) \perp \vec{a}$, find the angle between vector $\vec{a}$ and vector $\vec{b}$. | \frac{\pi}{3} | <｜begin▁of▁sentence｜><｜User｜>Given that $|\vec{a}| = 1$ and $\vec{b} = (1, \sqrt{3})$, and that $(\vec{b} - \vec{a}) \perp \vec{a}$, find the angle between vector $\vec{a}$ and vector $\vec{b}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here. It says that the magnitude of vector a is 1, so |a| = 1. Vector b is given as (1, sqrt(3)). Also, it's given that (b - a) is perpendicular to a. I need to find the angle between vector a and vector b.
Hmm, let's start by recalling some vector properties. If two vectors are pe... | official | v4_conceptual | 33,316 | 2,430 | feda398ba1eb7172 | \dfrac{\pi}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $|\\vec{a}| = 1$ and $\\vec{b} = (1, \\sqrt{3})$, and that $(\\vec{b} - \\vec{a}) \\perp \\vec{a}$, find the angle between vector $\\vec{a}$ and vector $\\vec{b}$.",
... | 2,443 |
<｜begin▁of▁sentence｜><｜User｜>In a version of SHORT BINGO, a $5\times5$ card has specific ranges for numbers placed in each column. In the first column, 5 distinct numbers must be chosen from the set $1-15$, but they must all be prime numbers. As before, the middle square is labeled as WILD and the other columns have sp... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In a version of SHORT BINGO, a $5\times5$ card has specific ranges for numbers placed in each column. In the first column, 5 distinct numbers must be chosen from the set $1-15$, but they must all be prime numbers. As before, the middle square is labeled as WILD and the other columns have specific number ranges as in th... | 720 | <｜begin▁of▁sentence｜><｜User｜>In a version of SHORT BINGO, a $5\times5$ card has specific ranges for numbers placed in each column. In the first column, 5 distinct numbers must be chosen from the set $1-15$, but they must all be prime numbers. As before, the middle square is labeled as WILD and the other columns have sp... | <think>
Okay, so I have this problem about a modified version of BINGO. Let me try to understand it step by step.
First, it's a 5x5 card, similar to the original BINGO, but with some differences. In the first column, instead of choosing any 5 distinct numbers from 1-15, they must all be prime numbers. Also, there's a ... | official | v4_conceptual | 28,880 | 1,500 | 118735cfaa8a3f4d | 720 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a version of SHORT BINGO, a $5\\times5$ card has specific ranges for numbers placed in each column. In the first column, 5 distinct numbers must be chosen from the set $1-15$,... | 1,513 |
<｜begin▁of▁sentence｜><｜User｜>In $\triangle ABC$, $\cos A= \frac{\sqrt{3}}{3}$, $c=\sqrt{3}$, and $a=3\sqrt{2}$. Find the value of $\sin C$ and the area of $\triangle ABC$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this triangle ABC, and I need to fi... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In $\triangle ABC$, $\cos A= \frac{\sqrt{3}}{3}$, $c=\sqrt{3}$, and $a=3\sqrt{2}$. Find the value of $\sin C$ and the area of $\triangle ABC$. | \frac{5\sqrt{2}}{2} | <｜begin▁of▁sentence｜><｜User｜>In $\triangle ABC$, $\cos A= \frac{\sqrt{3}}{3}$, $c=\sqrt{3}$, and $a=3\sqrt{2}$. Find the value of $\sin C$ and the area of $\triangle ABC$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this triangle ABC, and I need to find sin C and the area of the triangle. Let me write down the given information first:
- cos A = √3 / 3
- c = √3 (which I think is the side opposite angle C)
- a = 3√2 (which is the side opposite angle A)
Hmm, wait, let me make sure I understand the notation c... | official | v4_conceptual | 30,368 | 4,018 | 32099212112ed3c8 | \dfrac{5\sqrt{2}}{2} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, $\\cos A= \\frac{\\sqrt{3}}{3}$, $c=\\sqrt{3}$, and $a=3\\sqrt{2}$. Find the value of $\\sin C$ and the area of $\\triangle ABC$.",
"role": "user"
},
... | 4,031 |
<｜begin▁of▁sentence｜><｜User｜>Let \( x_{1}, x_{2} \) be the roots of the equation \( x^{2} - x - 3 = 0 \). Find \(\left(x_{1}^{5} - 20\right) \cdot \left(3 x_{2}^{4} - 2 x_{2} - 35\right)\). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem wher... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let \( x_{1}, x_{2} \) be the roots of the equation \( x^{2} - x - 3 = 0 \). Find \(\left(x_{1}^{5} - 20\right) \cdot \left(3 x_{2}^{4} - 2 x_{2} - 35\right)\). | -1063 | <｜begin▁of▁sentence｜><｜User｜>Let \( x_{1}, x_{2} \) be the roots of the equation \( x^{2} - x - 3 = 0 \). Find \(\left(x_{1}^{5} - 20\right) \cdot \left(3 x_{2}^{4} - 2 x_{2} - 35\right)\). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to find the value of \(\left(x_{1}^{5} - 20\right) \cdot \left(3 x_{2}^{4} - 2 x_{2} - 35\right)\), where \(x_{1}\) and \(x_{2}\) are the roots of the quadratic equation \(x^{2} - x - 3 = 0\). Hmm, let's try to figure this out step by step.
First, since \(x_{1}\) and \... | official | v4_conceptual | 3,715 | 2,809 | e72da0a726ec4f38 | -1063 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( x_{1}, x_{2} \\) be the roots of the equation \\( x^{2} - x - 3 = 0 \\). Find \\(\\left(x_{1}^{5} - 20\\right) \\cdot \\left(3 x_{2}^{4} - 2 x_{2} - 35\\right)\\).",
... | 2,822 |
<｜begin▁of▁sentence｜><｜User｜>Let \( y = (17 - x)(19 - x)(19 + x)(17 + x) \), where \( x \) is a real number. Find the smallest possible value of \( y \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: \( y = (17 - x)(19 - x)(19 + x)(17 + x)... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let \( y = (17 - x)(19 - x)(19 + x)(17 + x) \), where \( x \) is a real number. Find the smallest possible value of \( y \). | -1296 | <｜begin▁of▁sentence｜><｜User｜>Let \( y = (17 - x)(19 - x)(19 + x)(17 + x) \), where \( x \) is a real number. Find the smallest possible value of \( y \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: \( y = (17 - x)(19 - x)(19 + x)(17 + x) \), and I need to find the smallest possible value of \( y \). Hmm, let's try to figure this out step by step.
First, I notice that the expression for \( y \) is a product of four terms: \( (17 - x) \), \( (19 - x) \), \( (19 + x) \), and \(... | official | v4_conceptual | 4,682 | 2,937 | b127c3d88d3aa3b7 | -1296 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( y = (17 - x)(19 - x)(19 + x)(17 + x) \\), where \\( x \\) is a real number. Find the smallest possible value of \\( y \\).",
"role": "user"
},
{
"content": "<... | 2,950 |
<｜begin▁of▁sentence｜><｜User｜>Memories all must have at least one out of five different possible colors, two of which are red and green. Furthermore, they each can have at most two distinct colors. If all possible colorings are equally likely, what is the probability that a memory is at least partly green given that it ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Memories all must have at least one out of five different possible colors, two of which are red and green. Furthermore, they each can have at most two distinct colors. If all possible colorings are equally likely, what is the probability that a memory is at least partly green given that it has no red?
[i]Proposed by M... | 2/5 | <｜begin▁of▁sentence｜><｜User｜>Memories all must have at least one out of five different possible colors, two of which are red and green. Furthermore, they each can have at most two distinct colors. If all possible colorings are equally likely, what is the probability that a memory is at least partly green given that it ... | <think>
Okay, so I have this problem about memories, each of which can have at least one color out of five possible colors. Two of these colors are red and green. Each memory can have at most two distinct colors. We need to find the probability that a memory is at least partly green, given that it has no red. All possi... | official | v4_conceptual | 31,320 | 4,021 | bf77b9a9731db57d | \dfrac{2}{5} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Memories all must have at least one out of five different possible colors, two of which are red and green. Furthermore, they each can have at most two distinct colors. If all pos... | 4,034 |
<｜begin▁of▁sentence｜><｜User｜>Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the probabi... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC. | \frac{1}{3} | <｜begin▁of▁sentence｜><｜User｜>Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC, where point P is on side AB of triangle ABC. Hmm, let's break this down step by step.
First, let's visualize triangle ABC. Since P is on side AB, we can consider triangle ABC with poi... | official | v4_conceptual | 31,229 | 3,248 | 4f35b646c9d7d45b | \dfrac{1}{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC.",
"role": "user... | 3,261 |
<｜begin▁of▁sentence｜><｜User｜>Given $|\vec{a}|=1$, $|\vec{b}|= \sqrt{2}$, and $\vec{a} \perp (\vec{a} - \vec{b})$, find the angle between the vectors $\vec{a}$ and $\vec{b}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: given that the... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given $|\vec{a}|=1$, $|\vec{b}|= \sqrt{2}$, and $\vec{a} \perp (\vec{a} - \vec{b})$, find the angle between the vectors $\vec{a}$ and $\vec{b}$. | \frac{\pi}{4} | <｜begin▁of▁sentence｜><｜User｜>Given $|\vec{a}|=1$, $|\vec{b}|= \sqrt{2}$, and $\vec{a} \perp (\vec{a} - \vec{b})$, find the angle between the vectors $\vec{a}$ and $\vec{b}$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: given that the magnitude of vector a is 1, the magnitude of vector b is sqrt(2), and vector a is perpendicular to (a - b). I need to find the angle between vectors a and b. Hmm, let's break this down step by step.
First, let's recall that if two vectors are perpendicular, the... | official | v4_conceptual | 34,271 | 1,362 | 0c3ab0d18a06cc27 | \dfrac{\pi}{4} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $|\\vec{a}|=1$, $|\\vec{b}|= \\sqrt{2}$, and $\\vec{a} \\perp (\\vec{a} - \\vec{b})$, find the angle between the vectors $\\vec{a}$ and $\\vec{b}$.",
"role": "user"
}... | 1,375 |
<｜begin▁of▁sentence｜><｜User｜>How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to figure out how many integers between 1 a... | deepscaler_teacher_vllm_clean_v4_conceptual | math | How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers? | 750 | <｜begin▁of▁sentence｜><｜User｜>How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to figure out how many integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers. Hmm, let's start by understanding the problem.
First, the difference of squares. I remember that the difference of squares formula is a² - b², which can ... | official | v4_conceptual | 19,064 | 2,720 | 3daab75ca21693c6 | 750 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?",
"role": "user"
},
{
"content"... | 2,733 |
<｜begin▁of▁sentence｜><｜User｜>In how many ways can one choose distinct numbers a and b from {1, 2, 3, ..., 2005} such that a + b is a multiple of 5? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: I need to find the number of ways to choose t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | In how many ways can one choose distinct numbers a and b from {1, 2, 3, ..., 2005} such that a + b is a multiple of 5? | 401802 | <｜begin▁of▁sentence｜><｜User｜>In how many ways can one choose distinct numbers a and b from {1, 2, 3, ..., 2005} such that a + b is a multiple of 5? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: I need to find the number of ways to choose two distinct numbers a and b from the set {1, 2, 3, ..., 2005} such that their sum a + b is a multiple of 5. Hmm, that sounds like a combinatorics problem involving modular arithmetic. Let me try to break it down step by step.
First, I k... | official | v4_conceptual | 35,431 | 3,634 | b37802ad0b45e00a | 401802 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many ways can one choose distinct numbers a and b from {1, 2, 3, ..., 2005} such that a + b is a multiple of 5?",
"role": "user"
},
{
"content": "<think>\nOkay... | 3,647 |
<｜begin▁of▁sentence｜><｜User｜>What is the first nonzero digit to the right of the decimal point of the fraction $\frac{1}{129}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the first nonzero digit to the right of the decimal point in the fracti... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the first nonzero digit to the right of the decimal point of the fraction $\frac{1}{129}$? | 7 | <｜begin▁of▁sentence｜><｜User｜>What is the first nonzero digit to the right of the decimal point of the fraction $\frac{1}{129}$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the first nonzero digit to the right of the decimal point in the fraction 1/129. Hmm, let's see. I remember that when you divide 1 by a number, especially one that's not a multiple of 2 or 5, the decimal will be repeating. But maybe I don't need to go all the way to the repeating part. L... | official | v4_conceptual | 18,873 | 2,819 | d1ca4691420c07ce | 7 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the first nonzero digit to the right of the decimal point of the fraction $\\frac{1}{129}$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find... | 2,832 |
<｜begin▁of▁sentence｜><｜User｜>Given vectors $\overrightarrow {a} = (1, -3)$ and $\overrightarrow {b} = (-2, m)$, and $\overrightarrow {a}$ is perpendicular to ($\overrightarrow {a} - \overrightarrow {b}$).
(1) Find the value of the real number $m$;
(2) When $k\overrightarrow {a} + \overrightarrow {b}$ is parallel to... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given vectors $\overrightarrow {a} = (1, -3)$ and $\overrightarrow {b} = (-2, m)$, and $\overrightarrow {a}$ is perpendicular to ($\overrightarrow {a} - \overrightarrow {b}$).
(1) Find the value of the real number $m$;
(2) When $k\overrightarrow {a} + \overrightarrow {b}$ is parallel to $\overrightarrow {a} - \over... | -1 | <｜begin▁of▁sentence｜><｜User｜>Given vectors $\overrightarrow {a} = (1, -3)$ and $\overrightarrow {b} = (-2, m)$, and $\overrightarrow {a}$ is perpendicular to ($\overrightarrow {a} - \overrightarrow {b}$).
(1) Find the value of the real number $m$;
(2) When $k\overrightarrow {a} + \overrightarrow {b}$ is parallel to... | <think>
Okay, so I have this problem with two vectors, a and b. Vector a is given as (1, -3) and vector b is (-2, m). The problem has two parts.
First, part (1) says that vector a is perpendicular to (a - b). I need to find the value of m.
Alright, let's recall that if two vectors are perpendicular, their dot produ... | official | v4_conceptual | 30,814 | 2,008 | 85511c5d708f18b6 | -1 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow {a} = (1, -3)$ and $\\overrightarrow {b} = (-2, m)$, and $\\overrightarrow {a}$ is perpendicular to ($\\overrightarrow {a} - \\overrightarrow {b}$... | 2,021 |
<｜begin▁of▁sentence｜><｜User｜>Suppose that $a,b,$ and $c$ are positive integers satisfying $(a+b+c)^3 - a^3 - b^3 - c^3 = 150$. Find $a+b+c$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: given that a, b, and c are positive integers, a... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Suppose that $a,b,$ and $c$ are positive integers satisfying $(a+b+c)^3 - a^3 - b^3 - c^3 = 150$. Find $a+b+c$. | 6 | <｜begin▁of▁sentence｜><｜User｜>Suppose that $a,b,$ and $c$ are positive integers satisfying $(a+b+c)^3 - a^3 - b^3 - c^3 = 150$. Find $a+b+c$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: given that a, b, and c are positive integers, and they satisfy the equation (a + b + c)^3 - a^3 - b^3 - c^3 = 150. I need to find the value of a + b + c. Hmm, let's see.
First, I remember that there's a formula for expanding (a + b + c)^3. Let me recall it. I think it's somet... | official | v4_conceptual | 16,936 | 2,875 | eac1f2e2f74bc6b1 | 6 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $a,b,$ and $c$ are positive integers satisfying $(a+b+c)^3 - a^3 - b^3 - c^3 = 150$. Find $a+b+c$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I ... | 2,888 |
<｜begin▁of▁sentence｜><｜User｜>Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \angle AOB=60^\circ$ . A second circle is internally tangent to the first and tangent to both $ \overline{OA}$ and $ \overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle? Let'... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \angle AOB=60^\circ$ . A second circle is internally tangent to the first and tangent to both $ \overline{OA}$ and $ \overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle? | \frac{1}{9} | <｜begin▁of▁sentence｜><｜User｜>Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \angle AOB=60^\circ$ . A second circle is internally tangent to the first and tangent to both $ \overline{OA}$ and $ \overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle? Let'... | <think>
Okay, so I have this geometry problem here. Let me try to visualize it first. There's a circle with center O, and points A and B are on this circle. The angle AOB is 60 degrees. So, points A and B are on the circumference, and the angle between them at the center is 60 degrees. That means the arc AB is 60 degre... | official | v4_conceptual | 10,720 | 3,317 | 5f7077f77e3c5389 | \dfrac{1}{9} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \\angle AOB=60^\\circ$ . A second circle is internally tangent to the first and tangent to both $ \\overline{... | 3,330 |
<｜begin▁of▁sentence｜><｜User｜>On an old-fashioned bicycle the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes $100$ revolutions? Let's think step by step and output the final answer w... | deepscaler_teacher_vllm_clean_v4_conceptual | math | On an old-fashioned bicycle the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes $100$ revolutions? | 750 | <｜begin▁of▁sentence｜><｜User｜>On an old-fashioned bicycle the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes $100$ revolutions? Let's think step by step and output the final answer w... | <think>
Okay, so I have this problem about an old-fashioned bicycle. The front wheel has a radius of 2.5 feet, and the back wheel has a radius of 4 inches. The question is, if the front wheel makes 100 revolutions without any slippage, how many revolutions will the back wheel make?
Hmm, let's break this down. First, I... | official | v4_conceptual | 17,997 | 1,565 | 59cbdee5e073db96 | 750 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On an old-fashioned bicycle the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back... | 1,578 |
<｜begin▁of▁sentence｜><｜User｜>A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are there at the end of the $8^\te... | 48 | <｜begin▁of▁sentence｜><｜User｜>A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are t... | <think>
Okay, so I have this problem here about an organism that starts with three cells. Each cell splits into two cells every two days. This process continues for a total of 8 days, and I need to find out how many cells there are at the end of the 8th day. Hmm, let's break this down step by step.
First, the organism... | official | v4_conceptual | 17,000 | 1,327 | 35cf69a3568a1080 | 48 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and bec... | 1,340 |
<｜begin▁of▁sentence｜><｜User｜>Determine the value of $ab$ if $\log_8a+\log_4b^2=5$ and $\log_8b+\log_4a^2=7$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here where I need to find the value of \( ab \) given two logarithmic equations. The ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Determine the value of $ab$ if $\log_8a+\log_4b^2=5$ and $\log_8b+\log_4a^2=7$. | 512 | <｜begin▁of▁sentence｜><｜User｜>Determine the value of $ab$ if $\log_8a+\log_4b^2=5$ and $\log_8b+\log_4a^2=7$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here where I need to find the value of \( ab \) given two logarithmic equations. The equations are:
1. \( \log_8 a + \log_4 b^2 = 5 \)
2. \( \log_8 b + \log_4 a^2 = 7 \)
Hmm, let's see. I remember that logarithms with different bases can sometimes be converted to the same base to ... | official | v4_conceptual | 23,366 | 2,135 | 7bd003d09dade0e9 | 512 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of $ab$ if $\\log_8a+\\log_4b^2=5$ and $\\log_8b+\\log_4a^2=7$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here where... | 2,148 |
<｜begin▁of▁sentence｜><｜User｜>What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem: I need to find t... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? | 5 | <｜begin▁of▁sentence｜><｜User｜>What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: I need to find the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence where the terms are positive integers. Hmm, let's break this down step by step.
First, let me recall what an arithmetic sequence is. An arithmetic sequence is a ... | official | v4_conceptual | 39,011 | 2,756 | 3883a12a420cfd8e | 5 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers?",
"role": "user"
},
{
... | 2,769 |
<｜begin▁of▁sentence｜><｜User｜>Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this proble... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron. | \sqrt{3} | <｜begin▁of▁sentence｜><｜User｜>Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem: four of the eight vertices of a cube form a regular tetrahedron. I need to find the ratio of the surface area of the cube to the surface area of the tetrahedron. Hmm, let me try to visualize this.
First, let's recall what a cube is. A cube has 8 vertices, 12 edges, and all edges a... | official | v4_conceptual | 20,464 | 3,056 | 99271344d0d358af | \sqrt{3} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron.",
"role... | 3,069 |
<｜begin▁of▁sentence｜><｜User｜>Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the thr... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three factors, the probability t... | 76 | <｜begin▁of▁sentence｜><｜User｜>Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the thr... | <think>
Okay, so I need to solve this probability problem about Arnold and his three health risk factors A, B, and C. Let me try to parse the problem step by step.
First, the problem states:
- For each of the three factors (A, B, C), the probability that a randomly selected man has only that risk factor (and none of ... | official | v4_conceptual | 23,703 | 2,713 | f5ace00e030ac259 | 76 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly... | 2,726 |
<｜begin▁of▁sentence｜><｜User｜>Given the function $f(x)=\sin 2x+2\cos ^{2}x-1$.
$(1)$ Find the smallest positive period of $f(x)$;
$(2)$ When $x∈[0,\frac{π}{2}]$, find the minimum value of $f(x)$ and the corresponding value of the independent variable $x$. Let's think step by step and output the final answer within \... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the function $f(x)=\sin 2x+2\cos ^{2}x-1$.
$(1)$ Find the smallest positive period of $f(x)$;
$(2)$ When $x∈[0,\frac{π}{2}]$, find the minimum value of $f(x)$ and the corresponding value of the independent variable $x$. | \frac{\pi}{2} | <｜begin▁of▁sentence｜><｜User｜>Given the function $f(x)=\sin 2x+2\cos ^{2}x-1$.
$(1)$ Find the smallest positive period of $f(x)$;
$(2)$ When $x∈[0,\frac{π}{2}]$, find the minimum value of $f(x)$ and the corresponding value of the independent variable $x$. Let's think step by step and output the final answer within \... | <think>
Okay, so I have this function f(x) = sin(2x) + 2cos²x - 1, and I need to find its smallest positive period and then, when x is in [0, π/2], find the minimum value and the corresponding x. Let's take it step by step.
First, part (1): finding the smallest positive period of f(x). Hmm, the function is a combinati... | official | v4_conceptual | 13,741 | 3,388 | 7d3abb6b746c0489 | \dfrac{\pi}{2} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\sin 2x+2\\cos ^{2}x-1$. \n$(1)$ Find the smallest positive period of $f(x)$; \n$(2)$ When $x∈[0,\\frac{π}{2}]$, find the minimum value of $f(x)$ and ... | 3,401 |
<｜begin▁of▁sentence｜><｜User｜>Given that $a\in\{0,1,2\}$ and $b\in\{-1,1,3,5\}$, find the probability that the function $f(x)=ax^{2}-2bx$ is increasing on the interval $(1,+\infty)$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem where I need... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given that $a\in\{0,1,2\}$ and $b\in\{-1,1,3,5\}$, find the probability that the function $f(x)=ax^{2}-2bx$ is increasing on the interval $(1,+\infty)$. | \frac{5}{12} | <｜begin▁of▁sentence｜><｜User｜>Given that $a\in\{0,1,2\}$ and $b\in\{-1,1,3,5\}$, find the probability that the function $f(x)=ax^{2}-2bx$ is increasing on the interval $(1,+\infty)$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to find the probability that the function f(x) = a x² - 2b x is increasing on the interval (1, +∞). The variables a and b come from given sets: a is in {0,1,2}, and b is in {-1,1,3,5}. I need to find the probability, which means I have to figure out how many possible (a... | official | v4_conceptual | 15,075 | 3,326 | 4cdeb535eb73bca3 | \dfrac{5}{12} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a\\in\\{0,1,2\\}$ and $b\\in\\{-1,1,3,5\\}$, find the probability that the function $f(x)=ax^{2}-2bx$ is increasing on the interval $(1,+\\infty)$.",
"role": "use... | 3,339 |
<｜begin▁of▁sentence｜><｜User｜>The shortest distance for an ant to crawl along the surface of a rectangular box with length and width both being $6 \mathrm{~cm}$ from vertex $A$ to vertex $B$ is $20 \mathrm{~cm}$. What is the volume of this rectangular box in $\mathrm{cm}^{3}$? Let's think step by step and output the fin... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The shortest distance for an ant to crawl along the surface of a rectangular box with length and width both being $6 \mathrm{~cm}$ from vertex $A$ to vertex $B$ is $20 \mathrm{~cm}$. What is the volume of this rectangular box in $\mathrm{cm}^{3}$? | 576 | <｜begin▁of▁sentence｜><｜User｜>The shortest distance for an ant to crawl along the surface of a rectangular box with length and width both being $6 \mathrm{~cm}$ from vertex $A$ to vertex $B$ is $20 \mathrm{~cm}$. What is the volume of this rectangular box in $\mathrm{cm}^{3}$? Let's think step by step and output the fin... | <think>
Okay, so I have this problem about an ant crawling on the surface of a rectangular box. The box has length and width both equal to 6 cm. The ant starts at vertex A and crawls to vertex B along the surface, and the shortest distance it can crawl is 20 cm. I need to find the volume of the box. Hmm, let me think a... | official | v4_conceptual | 6,037 | 2,982 | e6a89dfa4e0b7a2f | 576 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The shortest distance for an ant to crawl along the surface of a rectangular box with length and width both being $6 \\mathrm{~cm}$ from vertex $A$ to vertex $B$ is $20 \\mathrm{... | 2,995 |
<｜begin▁of▁sentence｜><｜User｜>If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this equation: ab - 6a + 5b = 373, and I need to find the mi... | deepscaler_teacher_vllm_clean_v4_conceptual | math | If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$? | 31 | <｜begin▁of▁sentence｜><｜User｜>If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this equation: ab - 6a + 5b = 373, and I need to find the minimal possible value of |a - b| where a and b are positive integers. Hmm, let's see. I think I should try to rearrange the equation to make it easier to work with. Maybe factor it somehow or express one variable in terms of the other.
... | official | v4_conceptual | 37,281 | 2,195 | 090d68f460c7061a | 31 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$?",
"role": "user"
},
{
"content": "<think>\nOkay,... | 2,208 |
<｜begin▁of▁sentence｜><｜User｜>Given the hexadecimal system, determine the product of $A$ and $B$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem where I need to determine the product of A and B in the hexadecimal system. Hmm, hexadecimal, rig... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Given the hexadecimal system, determine the product of $A$ and $B$. | 6E | <｜begin▁of▁sentence｜><｜User｜>Given the hexadecimal system, determine the product of $A$ and $B$. Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to determine the product of A and B in the hexadecimal system. Hmm, hexadecimal, right? That's base 16, right? So each digit represents a value from 0 to 15, where A is 10 and B is 11 in decimal. Wait, actually, let me make sure. In hexadecimal, A is 10 and B is 11, cor... | official | v4_conceptual | 28,842 | 2,358 | 3468017b8c6ab417 | 6E | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hexadecimal system, determine the product of $A$ and $B$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem where I need to determine ... | 2,371 |
<｜begin▁of▁sentence｜><｜User｜>Voldemort bought a book for $\$5$. It was one-tenth of its original price. What was the original price in dollars? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: Voldemort bought a book for $5, and it was o... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Voldemort bought a book for $\$5$. It was one-tenth of its original price. What was the original price in dollars? | \$50 | <｜begin▁of▁sentence｜><｜User｜>Voldemort bought a book for $\$5$. It was one-tenth of its original price. What was the original price in dollars? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: Voldemort bought a book for $5, and it was one-tenth of its original price. I need to find out what the original price was. Hmm, let me break this down step by step.
First, let's understand what the problem is saying. Voldemort paid $5 for a book, and that amount is one-tenth... | official | v4_conceptual | 39,390 | 654 | 6258ff896fc98b9e | 50 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Voldemort bought a book for $\\$5$. It was one-tenth of its original price. What was the original price in dollars?",
"role": "user"
},
{
"content": "<think>\nOkay, s... | 667 |
<｜begin▁of▁sentence｜><｜User｜>If the sequence $\{a_n\}$ is defined by
$a_1=2$
$a_{n+1}=a_n+2n$
where $n\geq1$.
Then $a_{100}$ equals Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this sequence defined by a₁ = 2, and then each subsequent term is given by ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | If the sequence $\{a_n\}$ is defined by
$a_1=2$
$a_{n+1}=a_n+2n$
where $n\geq1$.
Then $a_{100}$ equals | 9902 | <｜begin▁of▁sentence｜><｜User｜>If the sequence $\{a_n\}$ is defined by
$a_1=2$
$a_{n+1}=a_n+2n$
where $n\geq1$.
Then $a_{100}$ equals Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this sequence defined by a₁ = 2, and then each subsequent term is given by a_{n+1} = a_n + 2n. I need to find a_{100}. Hmm, let me try to figure this out step by step.
First, let's write down the first few terms to see if I can spot a pattern or come up with a formula.
We know that a₁ = 2.
Th... | official | v4_conceptual | 20,656 | 1,829 | 909da26f325e929f | 9902 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the sequence $\\{a_n\\}$ is defined by\n$a_1=2$\n$a_{n+1}=a_n+2n$\nwhere $n\\geq1$.\nThen $a_{100}$ equals",
"role": "user"
},
{
"content": "<think>\nOkay, so I ha... | 1,842 |
<｜begin▁of▁sentence｜><｜User｜>A circle has an area of $\pi$ square units. What is the length of the circle's diameter, in units? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem here: A circle has an area of π square units. I need to find the l... | deepscaler_teacher_vllm_clean_v4_conceptual | math | A circle has an area of $\pi$ square units. What is the length of the circle's diameter, in units? | 2 | <｜begin▁of▁sentence｜><｜User｜>A circle has an area of $\pi$ square units. What is the length of the circle's diameter, in units? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem here: A circle has an area of π square units. I need to find the length of the circle's diameter. Hmm, let me remember how to find the area of a circle. I think the formula is A equals π times the radius squared, right? So, A = πr².
Since the area is given as π, I can set up the e... | official | v4_conceptual | 19,656 | 799 | 3ed1e5efbee80472 | 2 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle has an area of $\\pi$ square units. What is the length of the circle's diameter, in units?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this pr... | 812 |
<｜begin▁of▁sentence｜><｜User｜>Find the minimum value of the function \( f(x)=\cos 4x + 6\cos 3x + 17\cos 2x + 30\cos x \) for \( x \in \mathbb{R} \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this function \( f(x) = \cos 4x + 6\cos 3x + 17\cos 2x + 3... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Find the minimum value of the function \( f(x)=\cos 4x + 6\cos 3x + 17\cos 2x + 30\cos x \) for \( x \in \mathbb{R} \). | -18 | <｜begin▁of▁sentence｜><｜User｜>Find the minimum value of the function \( f(x)=\cos 4x + 6\cos 3x + 17\cos 2x + 30\cos x \) for \( x \in \mathbb{R} \). Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this function \( f(x) = \cos 4x + 6\cos 3x + 17\cos 2x + 30\cos x \), and I need to find its minimum value for real numbers \( x \). Hmm, this seems like a problem involving trigonometric functions. I remember that to find the minimum of such functions, sometimes it's helpful to express them in ... | official | v4_conceptual | 25,872 | 3,958 | e77c9f67b7fe0426 | -18 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of the function \\( f(x)=\\cos 4x + 6\\cos 3x + 17\\cos 2x + 30\\cos x \\) for \\( x \\in \\mathbb{R} \\).",
"role": "user"
},
{
"content": "<t... | 3,971 |
<｜begin▁of▁sentence｜><｜User｜>Below is a portion of the graph of an invertible function, $y=f(x)$:
[asy]
import graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-6.25,ymax=7.25;
pen cqcqcq=rgb(0.75,0.75,0.75);
/*grid*/ pen gs=linewidth(... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Below is a portion of the graph of an invertible function, $y=f(x)$:
[asy]
import graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-6.25,ymax=7.25;
pen cqcqcq=rgb(0.75,0.75,0.75);
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); ... | -2 | <｜begin▁of▁sentence｜><｜User｜>Below is a portion of the graph of an invertible function, $y=f(x)$:
[asy]
import graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-6.25,ymax=7.25;
pen cqcqcq=rgb(0.75,0.75,0.75);
/*grid*/ pen gs=linewidth(... | <think>
Okay, so I have this problem where there's a graph of an invertible function y = f(x). The problem states that f(a) = b and f(b) = 4. I need to find the value of a - b. Hmm, let's try to break this down step by step.
First, since the function is invertible, that means it's one-to-one, right? So, each x has a u... | official | v4_conceptual | 37,032 | 3,177 | bfc9ca2d6494b4cb | -2 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Below is a portion of the graph of an invertible function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds... | 3,190 |
<｜begin▁of▁sentence｜><｜User｜>The average of the numbers $1, 2, 3, \dots, 44, 45, x$ is $50x$. What is $x$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem where the average of the numbers from 1 to 45, and then adding another number x, is equ... | deepscaler_teacher_vllm_clean_v4_conceptual | math | The average of the numbers $1, 2, 3, \dots, 44, 45, x$ is $50x$. What is $x$? | \frac{1035}{2299} | <｜begin▁of▁sentence｜><｜User｜>The average of the numbers $1, 2, 3, \dots, 44, 45, x$ is $50x$. What is $x$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where the average of the numbers from 1 to 45, and then adding another number x, is equal to 50x. I need to find what x is. Hmm, let's break this down step by step.
First, let me understand what the problem is saying. We have the numbers from 1 to 45, and then we add another number... | official | v4_conceptual | 32,189 | 3,514 | e90c2da6b9932282 | \dfrac{1035}{2299} | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The average of the numbers $1, 2, 3, \\dots, 44, 45, x$ is $50x$. What is $x$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem where the avera... | 3,527 |
<｜begin▁of▁sentence｜><｜User｜>Let N = $69^5 + 5 \cdot 69^4 + 10 \cdot 69^3 + 10 \cdot 69^2 + 5 \cdot 69 + 1$. How many positive integers are factors of $N$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I have this problem where I need to find the number of pos... | deepscaler_teacher_vllm_clean_v4_conceptual | math | Let N = $69^5 + 5 \cdot 69^4 + 10 \cdot 69^3 + 10 \cdot 69^2 + 5 \cdot 69 + 1$. How many positive integers are factors of $N$? | 216 | <｜begin▁of▁sentence｜><｜User｜>Let N = $69^5 + 5 \cdot 69^4 + 10 \cdot 69^3 + 10 \cdot 69^2 + 5 \cdot 69 + 1$. How many positive integers are factors of $N$? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I have this problem where I need to find the number of positive integer factors of N, where N is given by the expression:
N = 69^5 + 5·69^4 + 10·69^3 + 10·69^2 + 5·69 + 1.
Hmm, that looks kind of complicated, but maybe it can be simplified or factored somehow. Let me see.
First, let me write down th... | official | v4_conceptual | 20,810 | 1,633 | cb5c3841070460d6 | 216 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let N = $69^5 + 5 \\cdot 69^4 + 10 \\cdot 69^3 + 10 \\cdot 69^2 + 5 \\cdot 69 + 1$. How many positive integers are factors of $N$?",
"role": "user"
},
{
"content": "<... | 1,646 |
<｜begin▁of▁sentence｜><｜User｜>What is the area of the smallest square that can contain a circle of radius 6? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think><think>
Okay, so I need to find the area of the smallest square that can contain a circle of radius 6. Hmm, let's think abo... | deepscaler_teacher_vllm_clean_v4_conceptual | math | What is the area of the smallest square that can contain a circle of radius 6? | 144 | <｜begin▁of▁sentence｜><｜User｜>What is the area of the smallest square that can contain a circle of radius 6? Let's think step by step and output the final answer within \boxed{}.<｜Assistant｜><think> | <think>
Okay, so I need to find the area of the smallest square that can contain a circle of radius 6. Hmm, let's think about this step by step.
First, I know that a square that can contain a circle must have sides that are at least as long as the diameter of the circle. Because if the square is too small, the circle ... | official | v4_conceptual | 9,150 | 710 | 22f9e78c8baa77f0 | 144 | true | 1 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area of the smallest square that can contain a circle of radius 6?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the area of the smal... | 723 |
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